Zero-Hopf Bifurcations of 3D Quadratic Jerk System

Zero-Hopf Bifurcations of 3D Quadratic Jerk System

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This paper is devoted to local bifurcations of three-dimensional (3D) quadratic jerk system.First, 3m speedglas 9002nc we start by analysing the saddle-node bifurcation.Then we introduce the concept of canonical system.Next, we study the transcritial bifurcation of canonical system.

Finally we study the zero-Hopf bifurcations of canonical system, which constitutes the core contributions of this paper.By averaging theory of first order, we prove that, at most, one limit cycle bifurcates from the zero-Hopf equilibrium.By averaging theory of second order, third order, and fourth order, we show that, at most, two limit cycles bifurcate from the equilibrium.Overall, this 15-eg1053cl paper can help to increase our understanding of local behaviour in the jerk dynamical system with quadratic non-linearity.