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

作者：Wei, Zhouchao^*; Moroz, Irene; Wang, Zhen; Sprott, Julien Clinton; Kapitaniak, Tomasz

来源：International Journal of Bifurcation and Chaos, 2016, 26(7): 1650125.

DOI：10.1142/S021812741650125X

• Kingni-Jafari system
• hidden attractor
• dynamics at infinity
• zero-Hopf bifurcation
• Hopf bifurcation

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 Poincare compactification of a polynomial vector field in R-3. 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.

• 出版日期2016-6-30
• 单位中国地质大学（北京）; 北京工业大学; 西京学院