Bifurcation analysis of Hénon-like maps

Abstract

The dynamic behaviour of a dynamical system, described by a planar map, is analytically and numerically explored. We examine the analytical conditions for the stability and bifurcation of the fixed points of the system and by using the numerical methods, we compute bifurcation curves of fixed points and cycles with orders up to five under variation of three parameters, and compute all codimension-1 and codimension-2 bifurcations on the corresponding curves. These curves form stability boundaries of various types of cycles which emanate around codimension-2 bifurcation points. Mathematical underpinnings and numerical simulations confirm our results and contribute to reveal further complex dynamical behaviours.