Quasicycles revisited: apparent sensitivity to initial conditions Export

@article{citeulike:994134, abstract = {Environmental noise is known to sustain cycles by perturbing a deterministic approach to equilibrium that is itself oscillatory. Quasicycles produced in this way display a regular period but varied amplitude. They were proposed by Nisbet and Gurney (Nature 263 (1976) 319) as one possible explanation for population fluctuations in nature. Here, we revisit quasicyclic dynamics from the perspective of nonlinear time series analysis. Time series are generated with a predator-prey model whose prey's growth rate is driven by environmental noise. A method for the analysis of short and noisy data provides evidence for sensitivity to initial conditions, with a global Lyapunov exponent often close to zero characteristic of populations `at the edge of chaos'. Results with methods restricted to long time series are consistent with a finite-dimensional attractor on which dynamics are sensitive to initial conditions. These results are compared with those previously obtained for quasicycles in an individual-based model with heterogeneous spatial distributions. Patterns of sensitivity to initial conditions are shown to differentiate phase-forgetting from phase-remembering quasicycles involving a periodic driver. The previously reported mode at zero of Lyapunov exponents in field and laboratory populations may reflect, in part, quasicyclic dynamics.}, author = {Pascual, Mercedes and Mazzega, Pierre}, booktitle = {Understanding the role of environmental vatiation in population and community dynamics}, citeulike-article-id = {994134}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/S0040-5809(03)00086-8}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6WXD-4967F9M-6/2/04b20aa2f3dc50801d984786c45bf792}, doi = {10.1016/S0040-5809(03)00086-8}, journal = {Theoretical Population Biology}, keywords = {dynamics, oscillation, population, quasi-cycle, stochastic}, month = {November}, number = {3}, pages = {385--395}, posted-at = {2006-12-14 07:34:08}, priority = {2}, title = {Quasicycles revisited: apparent sensitivity to initial conditions}, url = {http://dx.doi.org/10.1016/S0040-5809(03)00086-8}, volume = {64}, year = {2003} }

TY - JOUR ID - citeulike:994134 L3 - citeulike-article-id:994134 N2 - Environmental noise is known to sustain cycles by perturbing a deterministic approach to equilibrium that is itself oscillatory. Quasicycles produced in this way display a regular period but varied amplitude. They were proposed by Nisbet and Gurney (Nature 263 (1976) 319) as one possible explanation for population fluctuations in nature. Here, we revisit quasicyclic dynamics from the perspective of nonlinear time series analysis. Time series are generated with a predator-prey model whose prey's growth rate is driven by environmental noise. A method for the analysis of short and noisy data provides evidence for sensitivity to initial conditions, with a global Lyapunov exponent often close to zero characteristic of populations `at the edge of chaos'. Results with methods restricted to long time series are consistent with a finite-dimensional attractor on which dynamics are sensitive to initial conditions. These results are compared with those previously obtained for quasicycles in an individual-based model with heterogeneous spatial distributions. Patterns of sensitivity to initial conditions are shown to differentiate phase-forgetting from phase-remembering quasicycles involving a periodic driver. The previously reported mode at zero of Lyapunov exponents in field and laboratory populations may reflect, in part, quasicyclic dynamics. IS - 3 JF - Theoretical Population Biology EP - 395 TI - Quasicycles revisited: apparent sensitivity to initial conditions VL - 64 T2 - Understanding the role of environmental vatiation in population and community dynamics SP - 385 KW - dynamics KW - oscillation KW - population KW - quasi-cycle KW - stochastic AU - Pascual, Mercedes AU - Mazzega, Pierre PY - 2003/11// UR - http://dx.doi.org/10.1016/S0040-5809(03)00086-8 ER -