非局域耦合帐篷映像中的完全同步周期态

Completely synchronous periodic states in nonlocal coupled tent maps

研究了非局域耦合帐篷映像中的周期态,通过计算耦合系统的信息熵和同步序参量,发现系统中存在两类周期态,即非同步周期态和完全同步周期态。非同步周期态在空间呈现连续的波型分布,时间上也呈现周期性。其空间周期随着耦合半径的减小而减小,时间周期随系统参数的改变而变化。当完全同步态出现时,系统中各格点的动力学状态同步到单映像的非稳定周期态,这与以往的耦合系统中系统同步于单映像的稳定周期轨道有所不同。这类同步态的出现归因于格点间的动力学耦合,可以模拟神经元间触突耦合的丰富放电行为。

The periodic states in a system consisting of coupled tent maps with nonlocal interaction are investigated.The entropy and the synchronous order-parameters are calculated to distinguish different collective dynamical behaviors,which shows that there are two typical types of periodic state,i.e.,the nonsynchronous periodic states and complete synchronization periodic states.The nonsynchronous periodic states are in coherent states which have smooth wave-like profiles.The spatial period decreases as the coupling-length decreases,and the temporal period is determined by the system parameters.When the complete synchronous periodic state happens,the dynamical states of the nodes synchronize to some unstable periodic orbits.They are different from the conventional synchronous states,where the node dynamics synchronous to a stable periodic orbit of single map.This type of synchronized states is due to the interactions among the dynamics of the nodes and it can be used to simulate the rich discharge behavior of the synapses-coupling between neurons.