Results 101 to 110 of about 7,371 (144)
Shil'nikov Chaos control using Homoclinic orbits and the Newhouse region
, 2006 A method of controlling Shil'nikov's type chaos using windows that appear in the 1 dimensional bifurcation diagram when perturbations are applied, and using existence of stable homoclinic orbits near the unstable one is presented and applied to the ...
Furui, Sadataka, Niiya, Shohei
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Chaos and Control in Coronary Artery System
Discrete Dynamics in Nature and Society, 2012 Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method.
Yanxiang Shi
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A bifurcation analysis for the Lugiato-Lefever equation
, 2016 The Lugiato-Lefever equation is a cubic nonlinear Schr\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics.
Godey, Cyril
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Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues
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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Global homoclinic bifurcation for damped systems
Mathematische Zeitschrift, 1995 Recently, existence and other results have been obtained for the variational problem \((P^0)\) \(\ddot u= -V'(u, t)\), \(u(- \infty)= u(\infty)= 0\), \(\dot u(- \infty)= \dot u(\infty)= 0\), where \(u\in \mathbb{R}^p\), the potential \(V\) behaves roughly like \(V= -{1\over 2} |U|^2+ W(u, t)\) with \(W\) superquadratic and 1-periodic in \(t\).
openaire +3 more sources
Twisted and Nontwisted Bifurcations Induced by Diffusion
, 1996 We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop.
A. Lunardi +25 more
core +2 more sources
, 2010 We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (it has
Crovisier, Sylvain, Pujals, Enrique R.
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Scaling in activated escape of underdamped systems
, 2005 Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped.
A. P. Dmitriev +10 more
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Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations
Моделирование и анализ информационных систем, 2015 The feasibility of a known blue-sky bifurcation in a class of three-dimensional singularly perturbed systems of ordinary differential equations with one fast and two slow variables is studied.
S. D. Glyzin +2 more
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Some bifurcation methods of finding limit cycles
Mathematical Biosciences and Engineering, 2005 In this paper we outline some methods of finding limit cycles for planar autonomous systems with small parameter perturbations. Three ways of studying Hopf bifurcations and the method of Melnikov functions in studying Poincaré bifurcations are introduced
Maoan Han, Tonghua Zhang
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