Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos

Details Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos

2007-07-26

arxiv.org/abs/0707.3941v1

Nonlinear Sciences

Chaotic Dynamics

22 pages, 10 figures

Scientific paper

10.1063/1.2819537

We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha <2. In the continues limit the system's dynamics is described by the Ginzburg-Landau equation with complex coefficients. Such a system has a new parameter alpha that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics. We study different spatial-temporal patterns of the dynamics depending on alpha and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.

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