Synchronizing Chaos with Imperfections

Abstract

Previous research on nonlinear oscillator networks has shown that chaos synchronization is attainable for identical oscillators but deteriorates in the presence of parameter mismatches. Here, we identify regimes for which the opposite occurs and show that oscillator heterogeneity can synchronize chaos for conditions under which identical oscillators cannot. This effect is not limited to small mismatches and is observed for random oscillator heterogeneity on both homogeneous and heterogeneous network structures. The results are demonstrated experimentally using networks of Chua's oscillators and are further supported by numerical simulations and theoretical analysis. In particular, we propose a general mechanism based on heterogeneity-induced mode mixing that provides insights into the observed phenomenon. Since individual differences are ubiquitous and often unavoidable in real systems, it follows that such imperfections can be an unexpected source of synchronization stability.

Forced symmetry breaking as a mechanism for rogue bursts in a dissipative nonlinear dynamical lattice

“…Having examined the case of uniform coupling across the nodes of our ring, we now wish to explore the potential impact of heterogeneity in the lattice coupling, cf. [38][39][40]. Specifically, we suppose that the spatial coupling depends on the current value of z ± via the amplitude A according to…”

“…(1) possesses a substantial wealth of additional possible states as the relevant parameters vary [31,32]. In this light, a further study how such additional fixed points (especially so in the invariant subspace at infinite amplitude) may affect the dynamics of a diffusively coupled lattice system is certainly merited, as is a study of the effect of random coupling strengths between adjacent nodes, be these quenched or stochastically varying in time [38][39][40]. Moreover, the mechanism of extreme event production put forth herein is not restricted to one-dimensional lattices (as is often the case for integrable Hamiltonian systems) but generalizes naturally to higher dimensions, a topic also worth exploring in its own right.…”

Resilience in multiplex networks by addition of cross-repulsive links

“…Therefore, the stability of synchrony as a resilience [42] against parameter drift in local nodes of a network is to be established, i.e., the robustness of synchrony against parameter drift is the most desirable. Recently, encouraging reports are coming that create optimism about the constructive role of heterogeneity on synchrony in networks of nonidentical dynamical units [43], [44], [45], [46]. However, none of the reports addressed how to restore synchrony against a parameter drift.…”

Partial anti-synchronization of 4D laser system based on UDE

“…But most of the research on chaos only exists in the field of real numbers. In recent years, complex and fractional-order chaotic systems have become an important topic in the development of nonlinear science [4,5] . In recent years, chaos is more and more closely related to electronic information, computer engineering, biological engineering and other fields.…”