Classification of Bifurcations and Oscillations in Coupled BVP Oscillators

Bifurcation and Chaos in Coupled BVP oscillators

Non-monotonic changes and bifurcations in the period of coupled BVP oscillators due to noise and cyclic input

Effects of noise and cyclic input on the period of coupled Bonhoeffer-van der Pol (BVP) oscillators are studied with computer simulation. When the noise and cyclic input are added to a fast variable of a single BVP oscillator, the mean oscillation period is monotonically decreased as the strength of noise and the amplitude of input. When two oscillators are linearly coupled and the noise and cy...

Reviving oscillations in coupled nonlinear oscillators.

By introducing a processing delay in the coupling, we find that it can effectively annihilate the quenching of oscillation, amplitude death (AD), in a network of coupled oscillators by switching the stability of AD. It revives the oscillation in the AD regime to retain sustained rhythmic functioning of the networks, which is in sharp contrast to the propagation delay with the tendency to induce...

Two-cluster bifurcations in systems of globally pulse-coupled oscillators

For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via bifurcations. The coupling is modeled using the phaseresponse-curve (PRC), which measures the sensitivity of each oscillator’s phase to perturbations. For large system...

Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators

We consider the dynamics of networks of oscillators that are weakly dissipative perturbations of identical Hamiltonian oscillators with weak coupling. Suppose the Hamiltonian oscillators have angular frequency ω(α) when their energy is α. We address the problem of what happens in a neighbourhood of where dω/dα = 0; we refer to this as a point of isochronicity for the oscillators. If the couplin...