This paper considers nonlinear dynamics in an ensemble of uncoupled lasers, each being a limit-cycle oscillator, which are driven by the same external white Gaussian noise. As the external-noise strength increases, there is an onset of synchronization and then subsequent loss of synchrony. Local analysis of the laser equations shows that synchronization becomes unstable via stochastic bifurcati...

The slow passage problem, the slow variation of a control parameter, is explored in a model problem that posses several co-existing equilibria (fixed points, limit cycles and 2-tori), and these are either created or destroyed or change their stability as control parameters are varied through Hopf, Neimark-Sacker and torus break-up bifurcations. The slow passage through the Hopf bifurcation beha...

The continuous Bonhoeffer–van der Pol (BVP for short) oscillator is transformed into a mapbased BVP model by using the forward Euler scheme. At first, the bifurcations and chaos of the map-based BVP model are investigated when the step size varies as a bifurcation parameter. By using the fast-slow decomposition technique, a two-parameter bifurcation diagram is obtained to give insight into the ...

We investigate the saddle-node bifurcation and vibrational resonance in a fractional system that has an asymmetric bistable potential. Due to the asymmetric nature of the potential function, the response and its amplitude closely depend on the potential well where the motion takes place. And consequently for numerical simulations, the initial condition is a key and important factor. To overcome...

Parametrised contact-equivalence is successful for the understanding and classification of the qualitative local behaviour of bifurcation diagrams and their perturbations. Path formulation is an alternative point of view. It makes explicit the singular behaviour due to the core of the bifurcation germ (when the parameters vanish) from the effects of the way parameters enter. Here we show how pa...

In this paper we present a new version of Chen’s system — a piecewise linear Chen system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also mulistability, i.e. the existence of small parameter windows where, for some fixed bifurcation parameter and depending on initial...