ABSTRACT
A system showing chaotic behaviour undergoes transitions between nonchaotic and chaotic states in general. There are several ways in which a system undergoes a transition to chaos. Three typical ones are: through consecutive pitchfork bifurcations to chaos; through inverse tangent bifurcations or intermittency chaos to chaos; and through repeated Hopf bifurcations to chaos. The Feigenbaum route has been observed in many one-dimensional maps with smooth peaks. The route to chaos through period doubling phenomena is a typical scenario in the genesis of chaos, that is observed in many experiments. The stable periodic points produced by the bifurcation undergo successive pitchfork bifurcations within the window, leading to ‘small chaos’ there. The Feigenbaum route to chaos based on the infinite sequence of pitchfork bifurcations is seen in a wide class of maps.
