Results 11 to 20 of about 717,589 (231)
Homoclinic Orbits in Several Classes of Three-Dimensional Piecewise Affine Systems with Two Switching Planes [PDF]
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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Existence of homoclinic orbits for a class of nonlinear functional difference equations
Electronic Journal of Differential Equations, 2016 By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz ...
Xia Liu, Tao Zhou, Haiping Shi
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An example of chaotic behaviour in presence of a sliding homoclinic orbit [PDF]
, 2010 F. Battelli, Michal Feckan
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Chaotic motion around a black hole under minimal length effects
European Physical Journal C: Particles and Fields, 2020 We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit,
Xiaobo Guo +4 more
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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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Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation
Abstract and Applied Analysis, 2014 The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes ...
Fengjie Geng, Song Li
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Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Abstract and Applied Analysis, 2013 A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the ...
Tiansi Zhang, Xiaoxin Huang, Deming Zhu
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Моделирование и анализ информационных систем, 2015 We consider a finite-dimensional model of phase oscillators with inertia in the case of star configuration of coupling. The system of equations is reduced to a nonlinearly coupled system of pendulum equations.
V. N. Belykh +2 more
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Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
Abstract and Applied Analysis, 2013 We investigate the Shilnikov sense homoclinicity in a 3D system and consider the dynamical behaviors in vicinity of the principal homoclinic orbit emerging from a third order simplified system.
Gen Ge, Wang Wei
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The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues
Abstract and Applied Analysis, 2013 The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given ...
Xiaodong Li +3 more
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