We study the one-dimensional logistic map with control parameter perturbed by a small periodic function. In the pure constant case, scaling arguments are used to obtain the exponents related to the relaxation of the trajectories at the exchange of stability, period-doubling and tangent bifurcations. In particular, we evaluate the exponent z which describes the divergence of the relaxation time ...

In this work we consider the Colpitts oscillator as a paradigm for sinusoidal oscillation and we investigate its nonlinear dynamics. In particular, we carry out a two-parameter bifurcation analysis of a model of the oscillator. This analysis is conducted by combining numerical continuation techniques and normal form theory. First, we show that the birth of the harmonic cycle is associated with ...

Dynamical systems with a coupled cell network structure can display synchronous solutions, spectral degeneracies and anomalous bifurcation behavior. We explain these phenomena here for homogeneous networks, by showing that every homogeneous network dynamical system admits a semigroup of hidden symmetries. The synchronous solutions lie in the symmetry spaces of this semigroup and the spectral de...

The aim of the paper is to investigate the bifurcation behavior of the power-factor-correction (PFC) boost converter under a conventional peak current-mode control. The converter is operated in continuous-conduction mode. The bifurcation analysis performed by computer simulations reveals interesting effects of variation of some chosen parameters on the stability of the converter. The results ar...

We consider a one-parameter family of nonstrictly hyperbolic systems of conservation laws modeling three-phase flow in a porous medium. For a particular value of the parameter, the model has a shock wave solution that undergoes several bifurcations upon perturbation of its left and right states and the parameter. In this paper we use singularity theory and bifurcation theory of dynamical system...

We use the theory of coupled cell systems to analyze a neuronal network model for generalized rivalry posed by H. Wilson. We focus on the case of rivalry between two patterns and identify conditions under which large networks of n attributes and m intensity levels can reduce to a model consisting of two or three cells depending on whether or not the patterns have any attribute levels in common....

Hyperpolarization-activated cyclic nucleotide-gated cation current (Ih ) plays important roles in the achievement of many physiological/pathological functions in the nervous system by modulating the electrophysiological activities, such as the rebound (spike) to hyperpolarization stimulations, subthreshold membrane resonance to sinusoidal currents, and spike-timing precision to stochastic facto...