Results 1 to 10 of about 648 (183)
Examples and Counterexamples, 2022 Using a vector field in R4, we provide an example of a robust heteroclinic cycle between two equilibria that displays a mix of features exhibited by well-known types of low-dimensional heteroclinic structures, including simple, quasi-simple and pseudo ...
Sofia B.S.D. Castro, Alexander Lohse
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Heteroclinic Cycles Imply Chaos and Are Structurally Stable [PDF]
Discrete Dynamics in Nature and Society, 2021 This paper is concerned with the chaos of discrete dynamical systems. A new concept of heteroclinic cycles connecting expanding periodic points is raised, and by a novel method, we prove an invariant subsystem is topologically conjugate to the one-side ...
Xiaoying Wu
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Persistence of Heteroclinic Cycles Connecting Repellers in Banach Spaces [PDF]
Journal of Mathematics, 2022 This paper is concerned with persistence of heteroclinic cycles connecting repellers in Banach spaces. It is proved that if a map with a regular and nondegenerate heteroclinic cycle connecting repellers undergoes a small perturbation, then the perturbed ...
Zongcheng Li
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Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop [PDF]
Mathematics, 2023 This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m.
Erli Zhang, Stanford Shateyi
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Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system [PDF]
Scientific Reports, 2023 Little seems to be considered about the globally exponentially asymptotical stability of parabolic type equilibria and the existence of heteroclinic orbits in the Lorenz-like system with high-order nonlinear terms.
Haijun Wang +3 more
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A theoretical and computational study of heteroclinic cycles in Lotka-Volterra systems. [PDF]
J Math BiolBortolan MC +3 more
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Mathematical Biosciences and Engineering, 2023 In this paper, we consider the dynamics of a slow-fast Bazykin's model with piecewise-smooth Holling type Ⅰ functional response. We show that the model has Saddle-node bifurcation and Boundary equilibrium bifurcation.
Xiao Wu, Shuying Lu , Feng Xie
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Complex dynamics of a sub-quadratic Lorenz-like system
Open Physics, 2023 Motivated by the generic dynamical property of most quadratic Lorenz-type systems that the unstable manifolds of the origin tending to the stable manifold of nontrivial symmetrical equilibria forms a pair of heteroclinic orbits, this technical note ...
Li Zhenpeng +5 more
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Chaos criteria and chaotification schemes on a class of first-order partial difference equations
Mathematical Biosciences and Engineering, 2023 This article is involved in chaos criteria and chaotification schemes on one kind of first-order partial difference equations having non-periodic boundary conditions.
Zongcheng Li , Jin Li
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Nine Limit Cycles in a 5-Degree Polynomials Liénard System
Complexity, 2020 In this article, we study the limit cycles in a generalized 5-degree Liénard system. The undamped system has a polycycle composed of a homoclinic loop and a heteroclinic loop.
Junning Cai, Minzhi Wei, Hongying Zhu
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