Results 11 to 20 of about 3,877 (218)
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 symbolic system. Thus, heteroclinic cycles imply chaos in the sense of Devaney.
Xiaoying Wu
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Stable heteroclinic cycles and symbolic dynamics [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1994 Let S10, S11,...,S1n−1 be n circles. A rotation in n circles is a map f:∪i=0n−1S1i→∪ i=0n−1S1i which maps each circle onto another by a rotation. This particular type of interval exchange map arises naturally in bifurcation theory. In this paper we give a full description of the symbolic dynamics associated to such maps.
Lluı́s Alsedà +2 more
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An Introduction to Coupled Heteroclinic Cycles [PDF]
Progress of Theoretical Physics Supplement, 2003 Coupled heteroclinic cycles are introduced as a new class of coupled oscillator systems. As an example, we study a square lattice distribution of heteroclinic cycles and show the emergence of non-chaotic disordered patterns. A short analysis of them is also reported.
Masashi Tachikawa
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Heteroclinic cycles in lattice dynamical systems
Science in China Series A: Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
秦文新, QIAN MIN
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Control of noisy heteroclinic cycles
Physica D: Nonlinear Phenomena, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brianno Coller +2 more
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Stability of quasi-simple heteroclinic cycles [PDF]
Dynamical Systems, 2018 The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose connections are 1-dimensional and contained in flow-invariant spaces of equal dimension.
Liliana Garrido-da-Silva +1 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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Mathematics, 2021 The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine ...
Yanli Chen, Lei Wang, Xiaosong Yang
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Dynamics in a Predator–Prey Model with Cooperative Hunting and Allee Effect
Mathematics, 2021 This paper deals with a diffusive predator–prey model with two delays. First, we consider the local bifurcation and global dynamical behavior of the kinetic system, which is a predator–prey model with cooperative hunting and Allee effect.
Yanfei Du, Ben Niu, Junjie Wei
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