4-dimensional zero-Hopf bifurcation for polynomial differentials systems with cubic homogeneous nonlinearities via averaging theory [PDF]
International Journal of Dynamical Systems and Differential Equations, 2020 The averaging theory of second order shows that for polynomial differential systems in R4 with cubic homogeneous nonlinearities at least nine limit cycles can be born in a zero-Hopf bifurcation.
Feddaoui, Amina +2 more
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N-Dimensional Zero-Hopf Bifurcation of Polynomial Differential Systems via Averaging Theory of Second Order [PDF]
Journal of Dynamical and Control Systems, 2020 Using the averaging theory of second order, we study the limit cycles which bifurcate from a zero-Hopf equilibrium point of polynomial vector fields with cubic nonlinearities in Rn. We prove that there are at least 3n-2 limit cycles bifurcating from such zero-Hopf equilibrium points.
Kassa, Sara +2 more
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Periodic solutions for a four-dimensional hyperchaotic system
Advances in Difference Equations, 2020 In this paper, we show a zero-Hopf bifurcation in a four-dimensional smooth quadratic autonomous hyperchaotic system. Using averaging theory, we prove the existence of periodic orbits bifurcating from the zero-Hopf equilibrium located at the origin of ...
Jing Yang, Zhouchao Wei, Irene Moroz
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Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors
Complexity, 2021 Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method.
Mingshu Chen +3 more
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Zero-Hopf Bifurcations of 3D Quadratic Jerk System
Mathematics, 2020 This paper is devoted to local bifurcations of three-dimensional (3D) quadratic jerk system. First, we start by analysing the saddle-node bifurcation. Then we introduce the concept of canonical system.
Bo Sang, Bo Huang
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Zero-Hopf bifurcation and Hopf bifurcation for smooth Chua’s system
Advances in Difference Equations, 2018 Based on the fact that Chua’s system is a classic model system of electronic circuits, we first present modified Chua’s system with a smooth nonlinearity, described by a cubic polynomial in this paper. Then, we explore the distribution of the equilibrium
Junze Li, Yebei Liu, Zhouchao Wei
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Periodic orbits near equilibria via averaging theory of second order
Mathematical Modelling and Analysis, 2012 Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral.
Luis Barreira +2 more
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Limit cycle bifurcation from a zero-Hopf equilibrium for a class of 3-dimensional Kolmogorov systems
Partial Differential Equations in Applied MathematicsA zero-Hopf equilibrium point p of a 3-dimensional autonomous differential system in R3 is an equilibrium point such that the eigenvalues of the linear part of the system at p are 0 and ±ωi with ω≠0.
Chamseddine Bouaziz +2 more
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On the Periodic Solution for a Class of Perturbed a Hyper Jerk Memristive System
Sultan Qaboos University Journal for ScienceNonlinear dynamical systems with hidden attractors represent a recent and highly active area of research. In this work, the following novel class of four dimensional dynamical memristive vector field is considered [].
Niazy Hady Hussein +1 more
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Periodic orbits in hyperchaotic Chen systems
Electronic Journal of Differential Equations, 2015 In this work, we show a zero-Hopf bifurcation in a Hyperchaotic Chen system. Using averaging theory, we prove the existence of two periodic orbits bifurcating from the zero-Hopf equilibria located at the origin of the Hyperchaotic Chen system.
Susanna Maza
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