We consider a chain of nonlinear oscillators with long-range interaction of the type , where is a distance between oscillators and . In the continuous limit, the system’s dynamics is described by a fractional generalization of the Ginzburg-Landau equation with complex coefficients. Such a system has a new parameter that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics, especially near and . We study different spatiotemporal patterns of the dynamics depending on and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.
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Research Article| December 12 2007
Dynamics of the chain of forced oscillators with long-range interaction: From synchronization to chaos
G. M. Zaslavsky;
G. M. Zaslavsky
Courant Institute of Mathematical Sciences,
New York University, 251 Mercer St., New York, New York 10012, USA and Department of Physics,
New York University, 2-4 Washington Place, New York, New York 10003, USA
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V. E. Tarasov
G. M. Zaslavsky, M. Edelman, V. E. Tarasov; Dynamics of the chain of forced oscillators with long-range interaction: From synchronization to chaos. Chaos 1 December 2007; 17 (4): 043124. https://doi.org/10.1063/1.2819537
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