A periodically forced piecewise linear oscillator

Periodically forced piecewise-Linear Adaptive exponential Integrate-and-Fire Neuron

Although variability is a ubiquitous characteristic of the nervous system, under appropriate conditions neurons can generate precisely timed action potentials. Thus considerable attention has been given to the study of a neuron’s output in relation to its stimulus. In this study, we consider an increasingly popular spiking neuron model, the adaptive exponential integrateand-fire neuron. For ana...

An algebraically computable piecewise linear planar oscillator

A piecewise linear oscillator whose oscillation can be completely characterized by algebraic methods is studied. It represents up to the best of authors’s knowledge, the first example where all the oscillation properties can be determined for all the values of the bifurcation parameter, being not a perturbation of the harmonic oscillator. In fact, algebraic expressions for coordinates of repres...

Homoclinic trajectories and chaotic behaviour in a piecewise linear oscillator∗

Bifurcation analysis of a piecewise-linear impact oscillator with drift

We investigate the complex bifurcation scenarios occurring in the dynamic response of a piecewise-linear impact oscillator with drift, which is able to describe qualitatively the behaviour of impact drilling systems. This system has been extensively studied by numerical and analytical methods in the past, but its intricate bifurcation structure has largely remained unknown. For the bifurcation ...

Period-m Motions to Chaos in a Periodically Forced, Duffing Oscillator with a Time-Delayed Displacement

In this paper, periodic motions in a periodically excited, Duffing oscillator with a time-delayed displacement are investigated through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis. The time-delayed displacement is from the feedback control of displacement. The analytical bifurcation trees of period-1 motions to chaos i...