5,264 research outputs found
Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems
Systems that are not smooth can undergo bifurcations that are forbidden in
smooth systems. We review some of the phenomena that can occur for
piecewise-smooth, continuous maps and flows when a fixed point or an
equilibrium collides with a surface on which the system is not smooth. Much of
our understanding of these cases relies on a reduction to piecewise linearity
near the border-collision. We also review a number of codimension-two
bifurcations in which nonlinearity is important.Comment: pdfLaTeX, 9 figure
Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems
We reinvestigate the dynamical behavior of a first order scalar nonlinear
delay differential equation with piecewise linearity and identify several
interesting features in the nature of bifurcations and chaos associated with it
as a function of the delay time and external forcing parameters. In particular,
we point out that the fixed point solution exhibits a stability island in the
two parameter space of time delay and strength of nonlinearity. Significant
role played by transients in attaining steady state solutions is pointed out.
Various routes to chaos and existence of hyperchaos even for low values of time
delay which is evidenced by multiple positive Lyapunov exponents are brought
out. The study is extended to the case of two coupled systems, one with delay
and the other one without delay.Comment: 34 Pages, 14 Figure
Qualitative analysis of the dynamics of the time delayed Chua's circuit
IEEE TRANS. CIRCUITS SYST.
Generation of Multi-Scroll Attractors Without Equilibria Via Piecewise Linear Systems
In this paper we present a new class of dynamical system without equilibria
which possesses a multi scroll attractor. It is a piecewise-linear (PWL) system
which is simple, stable, displays chaotic behavior and serves as a model for
analogous non-linear systems. We test for chaos using the 0-1 Test for Chaos of
Ref.12.Comment: Corresponding Author: Eric Campos-Cant\'o
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