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Zero-Hopf bifurcation in a Chua system [PDF]
Nonlinear Analysis: Real World Applications, 2017 Agraïments: The first author is supported by the FAPESP-BRAZIL grants 2010/18015-6, 2012/05635-1, and 2013/25828-1. The second author is partially supported by FEDER-UNAB-10-4E-378, and a CAPES grant 88881.
D. Euzébio, Rodrigo, Llibre, Jaume
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Zero-Hopf bifurcation and Hopf bifurcation for smooth Chua’s system [PDF]
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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Zero-Hopf bifurcation in a 3D jerk system [PDF]
Nonlinear Analysis: Real World Applications, 2021 We consider the 3-D system defined by the jerk equation $\dddot{x} = -a \ddot{x} + x \dot{x}^2 -x^3 -b x + c \dot{x}$, with $a, b, c\in \mathbb{R}$. When $a=b=0$ and $c < 0$ the equilibrium point localized at the origin is a zero-Hopf equilibrium. We analyse the zero-Hopf Bifurcation that occur at this point when we persuade a quadratic perturbation
Francisco Braun, Ana C. Mereu
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Zero–Hopf bifurcation in a hyperchaotic Lorenz system [PDF]
Nonlinear Dynamics, 2013 We characterize the zero-Hopf bifurcation at the singular points of a parameter co-dimension four hyperchaotic Lorenz system. Using averaging theory, we find sufficient conditions so that at the bifurcation points two periodic solutions emerge and describe the stability of these orbits.
Cid-Montiel, Lorena +2 more
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Zero-Hopf Bifurcations of 3D Quadratic Jerk System [PDF]
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 in a Generalized Genesio Differential Equation [PDF]
Mathematics, 2021 The purpose of the present paper is to study the presence of bifurcations of zero-Hopf type at a generalized Genesio differential equation. More precisely, by transforming such differential equation in a first-order differential system in the three ...
Zouhair Diab +2 more
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Global dynamic characteristics of a piecewise smooth rotor/stator rubbing system with high speed. [PDF]
PLoS ONEIn this paper the global dynamic characteristics of a piecewise smooth rotor/stator rubbing system with high speed, which significantly differs from those of a low-speed system, are explored by numerical simulation and theoretical analysis.
Shunzeng Wang +3 more
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Slow onset of self-sustained oscillations in a fluctuating sideband-driven electromechanical resonator [PDF]
Scientific ReportsCritical slowing down of the dynamics of a system near bifurcation points leads to long recovery times towards stable states in response to perturbations.
B. Zhang +4 more
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Zero‐Hopf bifurcation in the FitzHugh–Nagumo system [PDF]
Mathematical Methods in the Applied Sciences, 2014 We characterize the values of the parameters for which a zero‐Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+, and P− in the FitzHugh–Nagumo system.We find two two‐parameter families of the FitzHugh–Nagumo system for which the equilibrium point at the origin is a zero‐Hopf equilibrium.
Euzébio, Rodrigo D. +2 more
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Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay
Nonlinear Analysis, 2021 In this paper, the Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay was explored. First, the conditions of the occurrence of Hopf-zero bifurcation were obtained by analyzing the distribution of eigenvalues in ...
Rina Su, Chunrui Zhang
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