For certain input power and wavelength settings, high Q-factor silicon-on-insulator rings self-pulsate. Thereby, they seem suited to emulate the behaviour of spiking neurons on a photonic chip. To gain insight in the possible excitation mechanisms a phase-plane analysis is needed. In this paper, we develop the theory needed to construct such phase portraits for a coupled mode theory description...

The present article deals with the inter specific competition and intra-specific competition among predator populations of a prey-dependent three component food chain model consisting of two competitive predator sharing one prey species as their food. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. Boundedness and dissipativeness of the system are e...

In this paper, we derive a four-dimensional ordinary differential equation (ODE) model representing the main interactions between Sox9, Sox10, Olig2 and several miRNAs, which drive process of (olygodendrocyte) differentiation. We utilize Lyapunov–Andronov theory to analyze its dynamical properties. Our results indicated that strength external signaling (morphogenic gradients shh bmp), transcrip...

Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise C1 map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations are not well understood. This paper considers a particular class of border-collision bifurcations, i.e., border-collision period-doubling bifu...

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction–diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions...

It is well known that dynamical systems defined by piecewise smooth functions exhibit several phenomena which cannot occur in smooth systems, such as for example, border collision bifurcations, sliding, chattering, etc. [di Bernardo et al., 2008]. One such phenomenon is the persistence of chaotic attractors under parameter perturbations, referred to as robust chaos [Banerjee et al., 1998]. In t...

Abstract Three local bifurcations in DC-DC converters are reviewed. They are period-doubling bifurcation, saddle-node bifurcation, and Neimark bifurcation. A general sampled-data model is employed to study types of loss of stability of the nominal (periodic) solution and their connection with local bifurcations. More accurate prediction of instability and bifurcation than using the averaging ap...

Bifurcation theory provides a classification of the expected ways in which the number and/or stability of invariant solutions (‘attractors’ and ‘repellors’) of nonlinear ordinary differential equations may change as parameter values are changed. The most common qualitative changes are ‘saddle-node’ bifurcations, ‘Hopf’ bifurcations, and ‘SNIPER’ bifurcations. At a saddle-node bifurcation, a pai...