Chaos in coupled Kerr-nonlinear parametric oscillators

Phase chaos in coupled oscillators.

A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos...

Bifurcation and Chaos in Coupled BVP oscillators

Synchronization of Chaos in Coupled Oscillators

This essay describes the experimental observation as well as numerical simulation and theory of synchronized chaos in systems of coupled oscillators. This work explores examples of this phenomenon in coupled electronic circuits and optoelectronic systems, as well as possible applications to secure communication.

Bifurcation and chaos in unidirectionally coupled oscillators

| Bifurcations of equilibrium points and limit cycles in unidirectionally coupled three oscillators are studied. According to their symmetrical properties, we classify equilibrium points and limit cycles into three and eight di erent types, respectively. Possible oscillations in unidirectional coupled three oscillators are presented by calculating Hopf bifurcation sets of equilibrium points. We...

Statistics of noise-driven coupled nonlinear oscillators: applications to systems with Kerr nonlinearity

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a determanistic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we sho...