CiteULike: coolger's library [34 articles]

Spatiotemporal Antiphase Dynamics in Coupled Extended Optical Media

E Louvergneaux — 2007-12-27T05:28:55-00:00

Physical Review Letters, Vol. 99, No. 26. (2007)

Experimental evidence of spatiotemporal antiphase dynamics is given for an extended system made of two liquid crystal slices that are optically coupled by two equal amplitude counterpropagating pumping beams. Theory and experiments carried out in a transverse one-dimensional configuration show that roll patterns are generated in each slice. These rolls are spatially in-phase or antiphase for a focusing or a defocusing nonlinearity type, respectively. These in-phase or antiphase dynamics remain robust even for complex spatiotemporal regimes such as dislocation regimes.

Combinatorics of feedback in cellular uptake and metabolism of small molecules

Sandeep Krishna — 2007-12-22T00:55:56-00:00

Proceedings of the National Academy of Sciences (19 December 2007), 0706231105.

We analyze the connection between structure and function for regulatory motifs associated with cellular uptake and usage of small molecules. Based on the boolean logic of the feedback we suggest four classes: the socialist, consumer, fashion, and collector motifs. We find that the socialist motif is good for homeostasis of a useful but potentially poisonous molecule, whereas the consumer motif is optimal for nutrition molecules. Accordingly, examples of these motifs are found in, respectively, the iron homeostasis system in various organisms and in the uptake of sugar molecules in bacteria. The remaining two motifs have no obvious analogs in small molecule regulation, but we illustrate their behavior using analogies to fashion and obesity. These extreme motifs could inspire construction of synthetic systems that exhibit bistable, history-dependent states, and homeostasis of flux (rather than concentration). 10.1073/pnas.0706231105

Mouse Ripply2 is downstream of Wnt3a and is dynamically expressed during somitogenesis

2007-10-17T14:54:37-00:00

Inhomogeneity-induced bifurcation of stationary and oscillatory pulses

Alain Prat — 2007-09-10T05:41:49-00:00

Physica D: Nonlinear Phenomena, Vol. 202, No. 3-4. (15 March 2005), pp. 177-199.

An excitable medium generally refers to a medium that is capable of generating traveling waves. It has been widely encountered in biology, chemistry and physics. Many excitable media have been modeled by systems of PDEs of the reaction-diffusion type. Excitable neural media are often modeled by integro-differential equations (IDEs). In both PDE and IDE models of excitable media, stationary spatial patterns of Turing's type can occur under certain conditions. Such patterns have been used to explain a variety of biological pattern formation processes including morphogenesis and hallucination. Here we study a pattern formation mechanism that is different from Turing's, called inhomogeneity-induced pattern formation. Such patterns can occur in an excitable medium either with an inhomogeneous but stationary forcing or a spatial variation in a model parameter. The interesting thing we found is: introducing a stationary bump into such a medium does not always produce just a simple bump-shaped output pattern. A complex bifurcation scenario can occur giving rise to the co-existence of multiple patterns. A stability analysis shows that the instability of such patterns often occurs through a Hopf bifurcation, giving rise to oscillatory pulse solutions. Such oscillatory pulses can behave like a pulse generator that emits traveling pulses periodically into the medium. Possible areas in biology where this theory can be applied will be discussed.

Drift and breakup of spiral waves in reaction-diffusion-mechanics systems

AV Panfilov — 2007-05-09T00:45:55-00:00

PNAS, Vol. 104, No. 19. (8 May 2007), pp. 7922-7926.

Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction-diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by substantial deformations of the medium. Here, we show that joint consideration of the RD equations with the equations of continuum mechanics for tissue deformations (RD-mechanics systems), yield important effects on spiral wave dynamics. We show that deformation can induce the breakup of spiral waves into complex spatiotemporal patterns. We also show that mechanics leads to spiral wave drift throughout the medium approaching dynamical attractors, which are determined by the parameters of the model and the size of the medium. We study mechanisms of these effects and discuss their applicability to the theory of cardiac arrhythmias. Overall, we demonstrate the importance of RD-mechanics systems for mathematics applied to life sciences. 10.1073/pnas.0701895104

Codimension-two bifurcation analysis on firing activities in Chay neuron model

Lixia Duan — 2006-07-15T04:55:27-00:00

Chaos, Solitons & Fractals, Vol. 30, No. 5. (December 2006), pp. 1172-1179.

Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.

Grazing phenomena in a periodically forced, friction-induced, linear oscillator

Albert Luo — 2006-04-24T00:14:01-00:00

Communications in Nonlinear Science and Numerical Simulation, Vol. 11, No. 7. (October 2006), pp. 777-802.

The criterion for grazing motions in a dry-friction oscillator is obtained from the local theory of non-smooth dynamical systems on the connectable and accessible domains. The generic mappings for such a dry-friction oscillator are also introduced. The sufficient and necessary conditions for grazing at the final states of mappings are expressed. The initial and final switching sets of grazing mapping, varying with system parameters, are illustrated for the grazing parametric characteristics. The initial and grazing, switching manifolds in the switching sets are defined through grazing mappings. Finally, numerical illustrations of grazing motions are very easily carried out with help of the analytical predictions. This paper provides a comprehensive investigation of grazing motions in the dry-friction oscillator for a better understanding of the grazing mechanism of such a discontinuous system. The investigation based on the local singularity theory is more intuitive and efficient than the discontinuous mapping techniques.

Continuous and discontinuous grazing bifurcations in impacting oscillators

Phanikrishna Thota — 2006-02-20T00:12:59-00:00

Physica D: Nonlinear Phenomena, Vol. 214, No. 2. (15 February 2006), pp. 187-197.

This paper seeks to formulate conditions for the persistence of a local attractor in the immediate vicinity of periodic and quasiperiodic grazing trajectories in an impacting mechanical system. A local analysis based on the discontinuity-mapping approach is employed to derive a normal-form description of the dynamics near the grazing trajectory. In agreement with previous studies of grazing periodic trajectories, it is found that the catastrophic loss of a local attractor and strong instability characteristic of grazing bifurcations is directly associated with the repeated application of a square-root term that appears to lowest order in the normal-form expansion. Specifically, it is found that the square-root term is absent in the description of the dynamics normal to a quasiperiodic trajectory covering a co-dimension-one invariant torus resulting in a piecewise linear description of the normal dynamics and, at most, a weak instability. In contrast, for co-dimension-two or higher, the square-root term is generically present in the normal dynamics. Here, however, the quasiperiodicity of the grazing motion implies that there is no upper limit to the time between impacts on nearby trajectories suggesting the persistence of a local attractor for some interval about the parameter value corresponding to grazing. The results of the analysis are illustrated through a series of model examples.

Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system

Zhanybai Zhusubaliyev — 2006-02-12T05:57:52-00:00

Physics Letters A, Vol. 351, No. 3. (27 February 2006), pp. 167-174.

Border-collision bifurcations arise when the periodic trajectory of a piecewise-smooth system under variation of a parameter crosses into a region with different dynamics. Considering a three-dimensional map describing the behavior of a DC/DC power converter, the Letter discusses a new type of border-collision bifurcation that leads to the birth of a "bilayered torus". This torus consists of the union of two saddle cycles, their unstable manifolds, and a stable focus cycle. When changing the parameters, the bilayered torus transforms through a border-collision bifurcation into a resonance torus containing the stable cycle and a saddle. The Letter also presents scenarios for torus destruction through homoclinic and heteroclinic tangencies.

Olfactory Computations and Network Oscillation

Alan Gelperin — 2006-02-08T23:53:23-00:00

J. Neurosci., Vol. 26, No. 6. (8 February 2006), pp. 1663-1668.

Block of Inferior Olive Gap Junctional Coupling Decreases Purkinje Cell Complex Spike Synchrony and Rhythmicity

Timothy Blenkinsop — 2006-02-08T23:47:02-00:00

J. Neurosci., Vol. 26, No. 6. (8 February 2006), pp. 1739-1748.

Inferior olivary (IO) neurons are electrotonically coupled by gap junctions. This coupling is thought to underlie synchronous complex spike (CS) activity generated by the olivocerebellar system in Purkinje cells, and also has been hypothesized to be necessary for IO neurons to generate spontaneous oscillatory activity. These characteristics of olivocerebellar activity have been proposed to be central to the role of this system in motor coordination. However, the relationship of gap junction coupling between IO neurons to synchronous and rhythmic CS activity has never been directly tested. Thus, to address this issue, multiple electrode recordings were obtained from crus 2a Purkinje cells, and carbenoxolone, a gap junction blocker, was injected into the IO. Carbenoxolone reduced CS synchrony by 50% overall, but in some experiments, >80% reductions were achieved. Carbenoxolone also reduced the average firing rate by 50%, suggesting that electrical coupling is a significant source of excitation for IO neurons. Moreover, carbenoxolone caused a reduction in the [~]10 Hz rhythmicity of CS activity, and this reduction was correlated with the extent to which the injection reduced CS synchrony. Lastly, carbenoxolone was found to reverse or prevent changes in synchrony that are normally induced by injection of GABAA and glutamate receptor antagonists into the IO, suggesting that the effects of these drugs on CS synchrony patterns require electrical coupling of IO neurons. In sum, our results provide direct evidence that electrical coupling of IO neurons underlies synchronous CS activity, and suggest important roles for this coupling in shaping other aspects of IO spiking patterns.

Design of bursting in a two-dimensional discrete-time neuron model

Hiroto Tanaka — 2006-01-21T13:24:22-00:00

Physics Letters A, Vol. 350, No. 3-4. (6 February 2006), pp. 228-231.

Alternating a quiescent state and a spiking one in a neuron is called bursting, which is one of important neuron activities. In this Letter, we will propose a simple design method for a bursting neuron model with a specified period and duty ratio of the bursting based on bifurcation theory. The neuron model has been proposed by the author et al. based on Aihara's chaotic neuron model. Mechanism of generating the bursting in the neuron model is a quasi-periodic oscillation with respect to internal states, which is caused from a Hopf bifurcation for a pair of two-periodic points. We also show an example derived by the proposed design method.

Estimation of critical behavior from the density of states in classical statistical models

A Malakis — 2005-08-10T23:40:30-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 70, No. 6. (2004)

We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling.

Behaviour of impact oscillator with soft and preloaded stop

Frantisek Peterka — 2006-01-16T09:00:19-00:00

Chaos, Solitons & Fractals, Vol. 18, No. 1. (September 2003), pp. 79-88.

New phenomena of the dynamics of oscillators with impacts, when the stiffness of the stop changes from zero to infinity, are described. Dynamics of one example of the system with soft impacts, as the model of the piercing machine, is explained in more detail by bifurcation diagrams, time series, phase trajectories and Poincare maps of periodic and chaotic impact motions. Optimal combinations of system parameters are found for the obtaining of maximum before-impact velocities.

Phenomena of subharmonic motions of oscillator with soft impacts

Frantisek Peterka — 2006-01-16T08:41:50-00:00

Chaos, Solitons & Fractals, Vol. 19, No. 5. (March 2004), pp. 1283-1290.

The excited, one degree of freedom mechanical system with soft impacts, characterised by triangle hysteresis loop, is investigated using numerical simulation. Small viscous damping is assumed. Phenomena of subharmonic motions are explained by regions of their existence and stability in the plane of dimensionless excitation frequency and static clearances. Bifurcation diagrams are evaluated during quasistationary changes of frequency by constant clearance.

Dynamics of an electronic impact oscillator

BK Clark — 2006-01-16T08:37:49-00:00

Physics Letters A, Vol. 318, No. 6. (24 November 2003), pp. 514-521.

Experimental measurements of an electronic impact oscillator that simulates a ball bouncing on a vibrating surface reveal interesting chaotic regimes that are consistent with the numerical simmulations. Correlation dimensions and Lyapunov exponents show good agreement between experimental and numerical results.

Neurodynamics of biased competition and cooperation for attention: a model with spiking neurons.

G Deco — 2005-10-08T21:54:01-00:00

J Neurophysiol, Vol. 94, No. 1. (July 2005), pp. 295-313.

Recent neurophysiological experiments have led to a promising "biased competition hypothesis" of the neural basis of attention. According to this hypothesis, attention appears as a sometimes nonlinear property that results from a top-down biasing effect that influences the competitive and cooperative interactions that work both within cortical areas and between cortical areas. In this paper we describe a detailed dynamical analysis of the synaptic and neuronal spiking mechanisms underlying biased competition. We perform a detailed analysis of the dynamical capabilities of the system by exploring the stationary attractors in the parameter space by a mean-field reduction consistent with the underlying synaptic and spiking dynamics. The nonstationary dynamical behavior, as measured in neuronal recording experiments, is studied by an integrate-and-fire model with realistic dynamics. This elucidates the role of cooperation and competition in the dynamics of biased competition and shows why feedback connections between cortical areas need optimally to be weaker by a factor of about 2.5 than the feedforward connections in an attentional network. We modeled the interaction between top-down attention and bottom-up stimulus contrast effects found neurophysiologically and showed that top-down attentional effects can be explained by external attention inputs biasing neurons to move to different parts of their nonlinear activation functions. Further, it is shown that, although NMDA nonlinear effects may be useful in attention, they are not necessary, with nonlinear effects (which may appear multiplicative) being produced in the way just described.

On multi-parametric bifurcations in a scalar piecewise-linear map

Viktor Avrutin — 2006-01-14T01:50:28-00:00

Nonlinearity, Vol. 19, No. 3. (2006), pp. 531-552.

In this work a one-dimensional piecewise-linear map is considered. The areas in the parameter space corresponding to specific periodic orbits are determined. Based on these results it is shown that the structure of the 2D and 3D parameter spaces can be simply described using the concept of multi-parametric bifurcations. It is demonstrated that an infinite number of two-parametric bifurcation lines starts at the origin of the 3D parameter space. Along each of these lines an infinite number of bifurcation planes starts, whereas the origin represents a three-parametric bifurcation.

Global bifurcation destroying the experimental torus T[sup 2]

T Pereira — 2006-01-12T08:42:33-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 73, No. 1. (2006)

We show experimentally the scenario of a two-frequency torus T2 breakdown, in which a global bifurcation occurs due to the collision of a torus with an unstable periodic orbit, creating a heteroclinic saddle connection, followed by an intermittent behavior.

Universal behavior of impact oscillators near grazing incidence

Wai Chin — 2006-01-10T02:56:00-00:00

Physics Letters A, Vol. 201, No. 2-3. (22 May 1995), pp. 197-204.

A grazing bifurcation is the bifurcation that takes place as a mechanical oscillator system evolves smoothly from a nonimpacting to an impacting state. This Letter summarizes different types of universal behavior associated with grazing bifurcations by consideration of a simple sinusoidally forced system.

Local analysis of co-dimension-one and co-dimension-two grazing bifurcations in impact microactuators

Harry Dankowicz — 2006-01-10T02:05:16-00:00

Physica D: Nonlinear Phenomena, Vol. 202, No. 3-4. (15 March 2005), pp. 238-257.

Impact microactuators rely on repeated collisions to generate gross displacements of a microelectromechanical machine element without the need for large applied forces. Their design and control rely on an understanding of the critical transition between non-impacting and impacting long-term system dynamics and the associated changes in system behavior. In this paper, we present three co-dimension-one, characteristically distinct transition scenarios associated with grazing conditions for a periodic response of an impact microactuator: a discontinuous jump to an impacting periodic response (associated with parameter hysteresis), a continuous transition to an impacting chaotic attractor, and a discontinuous jump to an impacting chaotic attractor. Using the concept of discontinuity mappings, a theoretical analysis is presented that predicts the character of each transition from a set of quantities that are computable in terms of system properties at grazing. Specifically, we show how this analysis can be applied to predict the bifurcation behavior on neighborhoods of two co-dimension-two bifurcation points that separate the co-dimension-one bifurcation scenarios. The predictions are validated against results from numerical simulations of a model impact microactuator.

A New Approach to the Stability Analysis of Boost Power-Factor-Correction Circuits

Sudip Mazumder — 2005-12-16T02:43:54-00:00

Journal of Vibration and Control, Vol. 9, No. 7. (1 July 2003), pp. 749-773.

We analyze the stability of a boost power-factor-correction (PFC) circuit using a hybrid model. We consider two multi-loop controllers to control the power stage. For each closed-loop system, we treat two separate cases: one for which the switching frequency is approaching infinity and the other for which it is finite but large. Unlike all previous analyses, the analysis in this paper investigates the stability of the converter in the saturated and unsaturated regions of operation. Using concepts of discontinuous systems, we show that the global existence of a smooth hypersurface for the boost PFC circuit is not possible. Subsequently, we develop conditions for the local existence of each of the closed-loop systems using a Lyapunov function. In other words, we derive the conditions for which a trajectory will reach a smooth hypersurface. If the trajectories do not reach the sliding surface, then the system saturates. As such, the stability of the period-one orbit is lost. Using the conditions for existence and the concept of equivalent control, we show why, for the second closed-loop system, the onset of the fast-scale instability occurs when the inductor current approaches zero. For this system, we show that the onset of the fast-scale instability near zero-inductor current occurs for a lower line voltage. Besides, when the peak of the line voltage approaches the bus voltage, the fast-scale instability may occur not only at the peak but also when the inductor current approaches zero. We develop a condition which ensures that the saturated region does not have any stable orbits. As such, a solution that leaves the sliding surface (if existence fails) cannot stabilize in the saturated region. Finally, we extend the analysis to the case in which the converter operates with a finite but large switching frequency. As such, the system has two fundamental frequencies: the switching and line frequencies. Hence, the dynamics of the system evolve on a torus. We show two different approaches to obtaining a solution for the closed-loop system. For the second closed-loop system, using the controller gain for the current loop as a bifurcation parameter, we show (using a Poincare map) the mechanism of the torus breakdown. If the mechanism of the torus breakdown is known, then, depending on the post-instability dynamics, a designer can optimize the design of the closed-loop converter.

Unfolding degenerate grazing dynamics in impact actuators

Xiaopeng Zhao — 2005-12-15T02:30:46-00:00

Nonlinearity, Vol. 19, No. 2. (2006), pp. 399-418.

In this paper, a selected analysis of the dynamics in an example impact microactuator is performed through a combination of numerical simulations and local analysis. Here, emphasis is placed on investigating the system response in the vicinity of the so-called grazing trajectories, i.e. motions that include zero-relative-velocity contact of the actuator parts, using the concept of discontinuity mappings that account for the effects of low-relative-velocity impacts and brief episodes of stick–slip motion. The analysis highlights the existence of isolated co-dimension-two grazing bifurcation points and the way in which these organize the behaviour of the impacting dynamics. In particular, it is shown how higher-order truncations of local maps of the near-grazing dynamics predict and enable the computation of global bifurcation curves emanating from such degenerate bifurcation points, thereby unfolding the near-grazing dynamics. Although the numerical results presented here are specific for the chosen model of an electrically driven and previously experimentally realized impact microactuator, the methodology generalizes naturally to arbitrary systems with impacts. Moreover, the qualitative nature of the near-grazing dynamics is expected to generalize to systems with similar nonlinearities.

Towards a comprehensive theory of brain activity:: Coupled oscillator systems under external forces

TD Frank — 2005-12-06T12:47:22-00:00

Physica D: Nonlinear Phenomena, Vol. 144, No. 1-2. (15 September 2000), pp. 62-86.

Recently, Jirsa et al. and Haken discussed a theory comprising the brain wave equation proposed by Nunez, the Wilson-Cowan/Ermentrout-Cowan model, and Hopfield networks. This theory was applied to model findings obtained in an experiment that relates brain activity and behavior, the so-called Julliard experiment. In previous works of Jirsa et al. and Frank et al. the focus was on the brain wave aspect. Recently, we conducted similar experiments. The results obtained are modeled in this paper in terms of coupled oscillator systems. Coupled oscillator systems are considered to represent the Wilson-Cowan/Ermentrout-Cowan-model aspect of the unifying theory. Building on a model proposed by Haken, Kelso, and Bunz and the theory of weakly coupled oscillators established by Winfree and by Kuramoto, we derive a nonlinear Fokker-Planck equation whose stationary solutions mimic the neocortical brain activity observed in our experiments.

Control of chaos: Methods and applications in engineering,

Alexander Fradkov — 2005-11-19T13:48:59-00:00

Annual Reviews in Control, Vol. 29, No. 1. (2005), pp. 33-56.

A survey of the emerging field termed "control of chaos" is given. Several major branches of research are discussed in detail: feedforward or "nonfeedback control" (based on periodic excitation of the system); "OGY method" (based on linearization of the Poincare map), "Pyragas method" (based on a time-delay feedback), traditional control engineering methods including linear, nonlinear and adaptive control, neural networks and fuzzy control. Some unsolved problems concerning the justification of chaos control methods are presented. Other directions of active research such as chaotic mixing, chaotization, etc. are outlined. Applications in various fields of engineering are discussed.

Signal Propagation and Logic Gating in Networks of Integrate-and-Fire Neurons

Tim Vogels — 2005-11-17T01:42:53-00:00

J. Neurosci., Vol. 25, No. 46. (16 November 2005), pp. 10786-10795.

Transmission of signals within the brain is essential for cognitive function, but it is not clear how neural circuits support reliable and accurate signal propagation over a sufficiently large dynamic range. Two modes of propagation have been studied: synfire chains, in which synchronous activity travels through feedforward layers of a neuronal network, and the propagation of fluctuations in firing rate across these layers. In both cases, a sufficient amount of noise, which was added to previous models from an external source, had to be included to support stable propagation. Sparse, randomly connected networks of spiking model neurons can generate chaotic patterns of activity. We investigate whether this activity, which is a more realistic noise source, is sufficient to allow for signal transmission. We find that, for rate-coded signals but not for synfire chains, such networks support robust and accurate signal reproduction through up to six layers if appropriate adjustments are made in synaptic strengths. We investigate the factors affecting transmission and show that multiple signals can propagate simultaneously along different pathways. Using this feature, we show how different types of logic gates can arise within the architecture of the random network through the strengthening of specific synapses.

Symmetry, Multistability, and Long-Range Interactions in Brain Development

Fred Wolf — 2005-11-08T07:40:37-00:00

Physical Review Letters, Vol. 95, No. 20. (2005)

An analytically tractable class of dynamical models for the pattern of contour detecting neurons in the visual cortex is introduced. A permutation symmetry of the model equations guarantees the emergence of contour detectors for all stimulus orientations. By this symmetry a large number of dynamically degenerate solutions exist that quantitatively reproduce the experimentally observed patterns. Long-range interactions are essential for the stability of these realistic solutions.

Polarization switching in a columnar liquid crystalline urea as studied by optical second-harmonic generation interferometry

Yoshinori Okada — 2005-08-10T23:31:04-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 72, No. 2. (2005)

The polar order and its switching characteristics have been investigated by means of optical second-harmonic generation interferometry in a compound N,N-bis(3,4,5-trialkoxylphenyl)urea (R=n-C16H33) being connected by intermolecular hydrogen bondings to form a columnar liquid crystalline phase. The polar structure is formed along the column by applying an electric field and is cooperatively switched by reversing the field. The polar order is relaxed to a nonpolar state within a few milliseconds by terminating the field. No macroscopic polar order exists at least in a range of a visible wavelength scale in the absence of a field.

Chaos and transient chaos in simple Hopfield neural networks

Xiao-Song Yang — 2005-11-01T14:52:03-00:00

Neurocomputing, Vol. 69, No. 1-3. (December 2005), pp. 232-241.

In this paper a class of simple chaotic Hopfield neural networks is presented, and a bifurcation from transient chaos to chaos is discussed.

Neuronal Oscillators in Aplysia californica that Demonstrate Weak Coupling In Vitro

Thorsten Peters — 2005-09-05T16:01:04-00:00

Physical Review Letters, Vol. 95, No. 10. (2005)

We report the first experimental demonstration of coherent population transfer, induced by stimulated Raman adiabatic passage, via continuum states. Population is transferred from the metastable state 2s 1S0 to the excited state 4s 1S0 in helium atoms in a two-photon process mediated by coherent interaction with the ionization continuum. While incoherent techniques usually do not permit any population transfer in such a process, we show that stimulated Raman adiabatic passage allows significant population transfer to take place also via ultrafast decay channels.

An organic thyristor

F Sawano — 2005-09-21T17:54:12-00:00

Nature, Vol. 437, No. 7058., pp. 522-524.

Saddle-node bifurcation of voltage profiles of small integrated AC/DC power systems

YK Fan — 2005-09-14T09:47:01-00:00

Power Engineering Society Summer Meeting, 2000. IEEE, Vol. 1 (2000), pp. 614-619 vol. 1.

Switch-mode converters are used for power transfer and load control in small integrated AC/DC power systems. In this paper, the authors develop a rectifier and inverter model for power flow analysis. These converters are operated in several control modes where rectifier and inverter may be either or both controlled. Depending on the control mode, they explore and compare different bus type models for the rectifier AC terminals. The developed models are integrated into an existing second-order power flow solver, which uses the Newton-Raphson-Seydel (N-R-S) technique to locate the saddle-node bifurcation point for multiple power flow solutions. They show in this paper that, depending on the control mode, a single DC link system may exhibit more than 2 power flow solutions. Based on stability analysis of the different branches of power flow solutions the feasible and controllable system operating points are determined. These studies yield estimates of maximum (steady state) loading points of small, integrated AC/DC power systems

AN ANALYTIC PICTURE OF NEURON OSCILLATIONS

Paul Phillipson — 2005-01-20T00:29:54-00:00

International Journal of Bifurcation and Chaos -- in Applied Sciences and Engineering, Vol. 14, No. 5. (May 2004), pp. 1539-1548.

Current induced oscillations of a space clamped neuron action potential demonstrates a bifurcation scenario originally encapsulated by the four-dimensional Hodgkin–Huxley equations. These oscillations were subsequently described by the two-dimensional FitzHugh–Nagumo Equations in close agreement with the Hodgkin–Huxley theory. It is shown that the FitzHugh–Nagumo equations can to close approximation be reduced to a generalized van der Pol oscillator externally driven by the current. The current functions as an external constant force driving the action potential. As a consequence approximate analytic expressions are derived which predict the bifurcation scenario, the amplitudes of the oscillations and the oscillation periods in terms of the current and the physiological constants of the FitzHugh–Nagumo model. A second reduction permits explicit analytic solution and results in a spiking model which can be multiply coupled and extended to include the dynamics of phase locking, entrainment and chaos characteristic of time-dependent synaptic inputs.

Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts

Albert Luo — 2005-03-10T02:13:09-00:00

Chaos, Solitons & Fractals, Vol. 24, No. 2. (April 2005), pp. 567-578.

In this paper, an idealized, piecewise linear system is presented to model the vibration of gear transmission systems. Periodic motions in a generalized, piecewise linear oscillator with perfectly plastic impacts are predicted analytically. The analytical predictions of periodic motion are based on the mapping structures, and the generic mappings based on the discontinuous boundaries are developed. This method for the analytical prediction of the periodic motions in non-smooth dynamic systems can give all possible periodic motions based on the adequate mapping structures. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems.