Sequence of Routes to Chaos in a Lorenz-Type System

Abstract EN

This paper reports a new bifurcation pattern observed in a Lorenz-type system.

The pattern is composed of a main bifurcation route to chaos ( n=1) and a sequence of sub-bifurcation routes with n=3,4,5,…,14 isolated sub-branches to chaos.

When n is odd, the n isolated sub-branches are from a period- n limit cycle, followed by twin period- n limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis.

When n is even, the n isolated sub-branches are from twin period- n/2 limit cycles, which become twin chaotic attractors via period-doubling bifurcations.

The paper also shows that the main route and the sub-routes can coexist peacefully by studying basins of attraction.