新的单参数混沌振子网络的同步化区域的转迁

本文针对一个新发现的单参数混沌系统作为节点动力学的动力网络，在给定某一内连矩阵情况下，研究了随节点动力学参数的连续变化，复杂动力网络同步化区域的演化与切换. 我们把这种网络同步化区域随节点动力学参数发生变化的现象称为网络同步化区域的分岔或转迁. 结果发现，对于某些内连矩阵，同步化区域不产生分岔现象，表明网络同步状态的稳定性不会因节点动力学参数的变化而发生改变；而对于某些内连矩阵，随节点动力学参数的逐渐增大，同步化区域主要出现了下面几种分岔或转迁模式：（1）无界-空集型的，（2）空集-有界-无界-有界-无界型的，（3）空集-无界-空集-无界-空集-无界型的，（4）空集-有界-无界-有界界-无界型的. 在这些分岔模式中，同步化区域随动力学参数的增大最后大都演化成无界型的，与统一混沌系统为节点动力学的网络的同步化区域的分岔模式有着显著差异. 这些现象表明：同一类型的节点动力学，不同的内连矩阵，矩阵网络同步化区域的分岔模式是不一样的；同一内连矩阵，不同类型的节点动力学，网络的同步区域的分岔模式也存在很多差异；不同的分岔模式，网络同步状态的稳定性也是不一样，它势必影响网络的同步能力.

Transitions of synchronized regions in new one-parameter chaotic oscillators networks

For the network with a newly discovered one-parameter chaotic system as its node dynamics, under some a fixed inner-linking matrix, the paper investigates the evolution and switching of synchronized region in complex dynamical networks with kinetic parameters in nodes dynamics, which is called as bifurcation or transition of networks synchronized regions. Investigations reveal that for some inner-linking matrices, there are no bifurcation phenomena of synchronized region, implying the stability of the network synchronous state can not be altered by varying dynamic parameter; While for some inner-linking matrices, the bifurcation emerges, and there are several mainly bifurcation patterns as follows: (1) unbounded-empty type, (2) empty-bounded-unbounded-bounded-unbounded type, (3) empty-unbounded-empty-unbound-empty-unbounded type, (4) empty-bounded-unbounded-bounded-unbounded type. Among these bifurcation patterns, with the increasing of dynamic parameter, synchronized region mostly ultimately evolves into the unbounded type except for the first type of pattern. There exists a significant difference between these patterns and those of network synchronized region with the same inner-linking matrix and the unified chaotic system as node dynamics. These indicate that for the same type of node dynamics, different inner-linking matrices can result in different bifurcation patterns of synchronized region; for an inner-linking matrix, different types of node dynamics can result in significant difference in bifurcation patterns of synchronized region; different bifurcation patterns can also result in different stability of network synchronous state which should affect the synchronizability of the networks.