Complex behavior in chains of nonlinear oscillators

Abstract

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions are sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

10 pages, 9 figures

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Cited by in corpus (6)

• Phenomenology of coupled non linear oscillators
• Computational capabilities at the edge of chaos for one dimensional system undergoing continuous transitions
• Complexity and transition to chaos in coupled Adler-type oscillators
• Behaviour of circular chains of nonlinear oscillators with Kuramoto-like local coupling
• Non-linear oscillators with Kuramoto-like local coupling: Complexity analysis and spatiotemporal pattern generation
• Correlation and collective behaviour in Adler-type locally coupled oscillators at the edge of chaos