Alternate Coupling Mechanism for Dynamical Quorum Sensing
Dynamical quorum sensing transition in a system, is the sudden change in its dynamics at a critical population size. We propose a novel coupling mechanism, the ?dominating surrounding effect?, that can lead to the dynamical quorum sensing transitions. This coupling mechanism has been implemented in both globally and locally coupled systems and found to be independent of the choice of the coupled variables (instantaneous or delayed). Because no local coupling scheme has been proposed so far that can illustrate dynamical quorum sensing in locally coupled systems, our local coupling scenario is a novel contribution. Although global coupling schemes for dynamical quorum sensing have been previously proposed, our global coupling scenario is different, as discussed in the text below. This coupling mechanism has been tested using a two-dimensional electrochemical model and a four dimensional biological model (Hodgkin?Huxley?s neuronal model). Two types of dynamical quorum sensing transitions, the emergence and the extinction of global oscillations in an ensemble of globally (all to all) and locally (1-D array with no flux boundary conditions) coupled oscillators, have been studied. Furthermore, the provoked spikes in the neuronal ensemble exhibit zero lag synchronization in the case of time delay and lag synchronization in the case of no-delay (instantaneous). In contrast, the induced oscillations are phase synchronized in the coupled electrochemical oscillators for both delay and no delay.