Results 41 to 50 of about 7,371 (144)
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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A Numerical Bifurcation Function for Homoclinic Orbits [PDF]
SIAM Journal on Numerical Analysis, 1998 Summary: The authors present a numerical method to locate periodic orbits near homoclinic orbits. Using a method of [\textit{X.-B. Lin}, Proc. R. Soc. Edinb., Ser. A 116, 295-325 (1990; Zbl 0714.34070)] and solutions of the adjoint variational equation, one gets a bifurcation function for periodic orbits, whose periods are asymptotic to infinity on ...
Ashwin, Peter, Mei, Zhen
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Bursting Oscillations in Shimizu-Morioka System with Slow-Varying Periodic Excitation
Shock and Vibration, 2018 The coupling effect of two different frequency scales between the exciting frequency and the natural frequency of the Shimizu-Morioka system with slow-varying periodic excitation is investigated.
Xindong Ma, Shuqian Cao
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Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback
Complexity, 2020 This work is focused on a shape memory alloy oscillator with delayed feedback. The main attention is to investigate the Bogdanov–Takens (B-T) bifurcation by choosing feedback parameters A1,2 and time delay τ.
Jinbin Wang, Lifeng Ma
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Hopf bifurcation control of the ML neuron model with Hc bifurcation type
Electronic Research Archive, 2022 It is shown that many neurological diseases are caused by the changes of firing patterns induced by bifurcations. Therefore, the bifurcation control may provide a potential therapeutic method of these neurodegenerative diseases.
Qinghua Zhu, Meng Li, Fang Han
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Invariant manifolds of the Bonhoeffer-van der Pol oscillator
, 2010 The stable and unstable manifolds of a saddle fixed point (SFP) of the Bonhoeffer-van der Pol oscillator are numerically studied. A correspondence between the existence of homoclinic tangencies (whic are related to the creation or destruction of Smale ...
Benítez, R., Bolós, V. J.
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Journal of Biological Dynamics, 2020 In this paper, Melnikov analysis of chaos in a simple SIR model with periodically or stochastically modulated nonlinear incidence rate and the effect of periodic and bounded noise on the chaotic motion of SIR model possessing homoclinic orbits are ...
Yanxiang Shi
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The Generalized Homoclinic Bifurcation
Journal of Differential Equations, 1994 The author considers a family \(X_ \lambda\) of vector fields that has at \(\lambda= 0\) a homoclinic loop of multiplicity \(n\). The aim of the paper is to present conditions of the versality of \(X\) in a neighborhood of the loop. For this, the author uses the representation of the displacement function given by \textit{R. Roussarie} [Bol. Soc. Bras.
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Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial
, 2012 A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor.
Abad A. +19 more
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On local and global aspects of the 1:4 resonance in the conservative cubic H\'enon maps [PDF]
, 2017 We study the 1:4 resonance for the conservative cubic H\'enon maps $\mathbf{C}_\pm$ with positive and negative cubic term. These maps show up different bifurcation structures both for fixed points with eigenvalues $\pm i$ and for 4-periodic orbits. While
Gonchenko, M. +3 more
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