Results 11 to 20 of about 401 (174)
Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues [PDF]
The Scientific World Journal, 2014 By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the ...
Yinlai Jin +5 more
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Resonance Bifurcations of Robust Heteroclinic Networks [PDF]
SIAM Journal on Applied Dynamical Systems, 2012 46 pages, 20 figures. Supplementary material (two animated gifs) can be found on http://www.maths.leeds.ac.uk/~alastair/papers/KPR_res_net_abs ...
Vivien Kirk +2 more
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Dissecting a Resonance Wedge on Heteroclinic Bifurcations [PDF]
Journal of Statistical Physics, 2021 This article studies routes to chaos occurring within a resonance wedge for a 3-parametric family of differential equations acting on a 3-sphere. Our starting point is an autonomous vector field whose flow exhibits a weakly attracting heteroclinic network made by two 1-dimensional connections and a 2-dimensional separatrix between two equilibria with ...
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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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Homoclinic and Heteroclinic Bifurcations in Vector Fields [PDF]
, 2010 An overview of homoclinic and heteroclinic bifurcation theory for autonomous vector fields is given. Specifically, homoclinic and heteroclinic bifurcations of codimension one and two in generic, equivariant, reversible, and conservative systems are reviewed, and results pertaining to the existence of multi-round homoclinic and periodic orbits and of ...
Homburg, A.J., Sandstede, B.
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Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators
Shock and Vibration, 2022 The vibrating system of a class of linkage-slider structure is considered, and its initial-sensitive dynamical behaviors such as safe jump, locking instability, and chaos are studied. First, static bifurcation of the dynamical system is discussed.
Bo Qin, Huilin Shang, Huimin Jiang
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Global Bifurcation Behaviors and Control in a Class of Bilateral MEMS Resonators
Fractal and Fractional, 2022 The investigation of global bifurcation behaviors the vibrating structures of micro-electromechanical systems (MEMS) has received substantial attention. This paper considers the vibrating system of a typical bilateral MEMS resonator containing fractional
Yijun Zhu, Huilin Shang
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Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria
The Scientific World Journal, 2014 The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Fengjie Geng, Junfang Zhao
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Bifurcation analysis of a two-dimensional discrete Hindmarsh–Rose type model
Advances in Difference Equations, 2019 In this paper, bifurcation analysis of a discrete Hindmarsh–Rose model is carried out in the plane. This paper shows that the model undergoes a flip bifurcation, a Neimark–Sacker bifurcation, and 1:2 $1:2$ resonance which includes a pitchfork bifurcation,
Bo Li, Qizhi He
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Dynamics of a Predator–Prey Model with the Additive Predation in Prey
Mathematics, 2022 In this paper, we consider a predator–prey model, in which the prey’s growth is affected by the additive predation of its potential predators. Due to the additive predation term in prey, the model may exhibit the cases of the strong Allee effect, weak ...
Dingyong Bai, Xiaoxuan Zhang
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