Yanchuk S, Perlikowski P, Wolfrum M, Stefański A, Kapitaniak T
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
Division of Dynamics, Technical University of Lodz, 90-924 Lodz, Poland.
Chaos. 2015 Mar;25(3):033113. doi: 10.1063/1.4915941.
We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state and close-by solutions in the limit of a large number of nodes. Studying numerically an example of unidirectionally coupled Duffing oscillators, we observe a coupling induced transition to collective spatio-temporal chaos, which can be understood using the derived amplitude equations.
我们研究了在环形结构中耦合的大量相同振子阵列中，耦合引起的失稳现象。其中，环形结构中的振子通过多种与多个相邻振子的不同类型相互作用来实现耦合。我们推导了一个金兹堡 - 朗道型的振幅方程，该方程描述了在大量节点的极限情况下，均匀稳态及附近解的失稳情况。通过对单向耦合达芬振子的一个示例进行数值研究，我们观察到耦合诱导的向集体时空混沌的转变，这可以用推导得到的振幅方程来理解。
