Dynamics at Infinity, Degenerate Hopf and Zero-Hopf Bifurcation for Kingni–Jafari System with Hidden Attractors

Abstract

To understand the complex dynamics of Kingni–Jafari system with hidden attractors, the first objective of this paper is to study the global dynamics, and give a complete description of the dynamics of Kingni–Jafari system at infinity by using the Poincaré compactification of a polynomial vector field in [Formula: see text]. The second objective of this paper is to prove the existence of periodic solutions in the Kingni–Jafari system by classical Hopf bifurcation and degenerate Hopf bifurcation. Moreover, based on averaging theory, a small amplitude periodic solution that bifurcates from a zero-Hopf equilibrium was derived in the Kingni–Jafari system. The theoretical analysis and simulations demonstrate the rich dynamics of the system.