Zero-Hopf bifurcation in the Volterra-Gause system of predator-prey type
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DOI: 10.1002/mma.4569
Abstract: We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the… read more here.
Keywords: volterra gause; predator prey; prey type; gause system ... See more keywords
N-Dimensional Zero-Hopf Bifurcation of Polynomial Differential Systems via Averaging Theory of Second Order
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-020-09501-6
Abstract: 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 ℝ n $\mathbb {R}^{n}$ . We prove that… read more here.
Keywords: averaging theory; second order; limit cycles; theory second ... See more keywords
Transcritical and zero-Hopf bifurcations in the Genesio system
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DOI: 10.1007/s11071-016-3259-2
Abstract: In this paper we study the existence of transcritical and zero-Hopf bifurcations of the third-order ordinary differential equation $${\dddot{x}} + a {\ddot{x}} + b {\dot{x}} + c x - x^2 = 0$$x⃛+ax¨+bx˙+cx-x2=0, called the Genesio… read more here.
Keywords: bifurcations genesio; system; hopf bifurcations; zero hopf ... See more keywords
Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
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DOI: 10.1007/s12591-017-0375-5
Abstract: We study the zero-Hopf bifurcation of the third-order differential equations $$\begin{aligned} x^{\prime \prime \prime }+ (a_{1}x+a_{0})x^{\prime \prime }+ (b_{1}x+b_{0})x^{\prime }+x^{2} =0, \end{aligned}$$x″′+(a1x+a0)x″+(b1x+b0)x′+x2=0,where $$a_{0}$$a0, $$a_{1}$$a1, $$b_{0}$$b0 and $$b_{1}$$b1 are real parameters. The prime denotes derivative with… read more here.
Keywords: order differential; zero hopf; differential equations; prime prime ... See more keywords
Algebraic Analysis of Zero-Hopf Bifurcation in a Chua System
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DOI: 10.3390/sym14051036
Abstract: This article first studies the stability conditions of a Chua system depending on six parameters. After, using the averaging method, as well as the methods of the Gröbner basis and real solution classification, we provide… read more here.
Keywords: system; analysis zero; algebraic analysis; zero hopf ... See more keywords