From Order to Chaos: Bifurcation Scenarios (Part I)

Abstract

A dynamical system (DS) displays its nonlinear properties in different ways when system control parameters are varied. But as a rule, when the influence of nonlinearity increases, the dynamical regime becomes more complicated. Simple attractors in the phase space of a dissipative system are replaced by more complicated ones. Under certain conditions, nonlinearity can lead to the onset of dynamical chaos. Moving along a relevant direction in the parameter space, a sequence of bifurcations can be observed, resulting in the appearance of a chaotic attractor. Such typical bifurcation sequences are called bifurcation mechanisms, or scenarios of the transition to chaos.