Results 21 to 30 of about 5,968 (173)
Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems
Abstract and Applied Analysis, 2012 The bifurcations near a primary homoclinic orbit to a saddle-center are investigated in a 4-dimensional reversible system. By establishing a new kind of local moving frame along the primary homoclinic orbit and using the Melnikov functions, the existence
Zhiqin Qiao, Yancong Xu
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On the Homoclinic Orbits of the Lü System [PDF]
International Journal of Bifurcation and Chaos, 2017 In this paper, the existence of homoclinic orbits of the equilibrium point [Formula: see text] is demonstrated in the case of the Lü system for parameter values not reported by G. A. Leonov. In addition, some simulations are shown that agree with our theoretical analysis.
Martha Alvarez-Ramírez +1 more
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Homoclinic chaos in the Rössler model [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020 We study the origin of homoclinic chaos in the classical 3D model proposed by Rössler in 1976. Of our particular interest are the convoluted bifurcations of the Shilnikov saddle-foci and how their synergy determines the global bifurcation unfolding of the model, along with transformations of its chaotic attractors.
Semyon Malykh +4 more
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The Nehari manifold method for discrete fractional p-Laplacian equations
Advances in Difference Equations, 2020 The aim of this paper is to investigate the multiplicity of homoclinic solutions for a discrete fractional difference equation. First, we give a variational framework to a discrete fractional p-Laplacian equation.
Xuewei Ju, Hu Die, Mingqi Xiang
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Scarring by Homoclinic and Heteroclinic Orbits [PDF]
Physical Review Letters, 2006 In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated closed circuits in phase space are properly quantized, thus introducing strong quantum correlations.
Wisniacki, D. A. +3 more
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Frontiers in Physics, 2022 A class of generalized homoclinic solutions of the nonlinear Schrödinger (NLS) equation in 1+1 dimensions is studied. These are homoclinic breathers that are shown to be derivable from the ratio of Riemann theta functions for the genus-2 solutions of ...
Alfred R. Osborne
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Homoclinic points and moduli [PDF]
Ergodic Theory and Dynamical Systems, 1989 AbstractIn this paper we study some conjugacy invariants (moduli) for discrete two dimensional dynamical systems, with a homoclinic tangency. We show that the modulus obtained by Palis in the heteroclinic case also turns up in the case considered here. We also present two new conjugacy invariants.
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The Related Extension and Application of the Ši'lnikov Theorem
Journal of Applied Mathematics, 2013 The traditional Ši'lnikov theorems provide analytic criteria for proving the existence of chaos in high-dimensional autonomous systems. We have established one extended version of the Ši'lnikov homoclinic theorem and have given a set of sufficient ...
Baoying Chen
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Bursting Oscillations in General Coupled Systems: A Review
Mathematics, 2023 In this paper, the bursting oscillation phenomenon in coupled systems with two time scales is introduced. Firstly, several types of bifurcation are briefly introduced: fold bifurcation, Hopf bifurcation, fold limit cycle bifurcation, homoclinic ...
Danjin Zhang, Youhua Qian
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Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
Shock and Vibration, 2016 The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure.
Yang-Yang Chen +2 more
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