Results 31 to 40 of about 5,968 (173)
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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Robust homoclinic orbits in planar systems with Preisach hysteresis operator [PDF]
, 2016 We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time.
Pimenov, Alexander, Rachinskii, Dmitrii
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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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Continuum-wise expansive homoclinic classes for robust dynamical systems
Advances in Difference Equations, 2019 In the study, we consider continuum-wise expansiveness for the homoclinic class of a kind of C1 $C^{1}$-robustly expansive dynamical system. First, we show that if the homoclinic class H(p,f) $H(p, f)$, which contains a hyperbolic periodic point p, is R ...
Manseob Lee
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 We obtain an existence theorem of nonzero solution for a class of bounded selfadjoint operator equations. The main result contains as a special case the existence result of a nontrivial homoclinic orbit of a class of Hamiltonian systems by Coti Zelati ...
Mingliang Song, Runzhen Li
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Homoclinic bifurcations in a planar dynamical system
, 2022 S.1183-1191The homoclinic bifurcation properties of a planar dynamical system are analyzed and the corresponding bifurcation diagram is presented. The occurrence of two Bogdanov-Takens bifurcation points provides two local existing curves of homoclinic ...
Kuepper, T., Giannakopoulos, F., Zou, Y.
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Dynamics of a state-dependent delay-differential equation
Electronic Journal of Qualitative Theory of Differential EquationsWe present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model.
Tomas Gedeon +4 more
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Homoclinic and heteroclinic solutions to a hepatitis C evolution model
Open Mathematics, 2018 Homoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper.
Telksnys Tadas +4 more
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Synchronization of "Hopf/homoclinic" bursting with "SubHopf/homoclinic" bursting
Acta Physica Sinica, 2013 Taking the modified Morris-Lecar neuron model for example, we consider the synchronous behaviour between "Hopf/homoclinic" bursting and "SubHopf/homoclinic" bursting. Firstly, the synchronization between two coupled bursting neurons with the same topological type is investigated numerically, and the results show that the coupling strength reaching the ...
null Wang Fu-Xia, null Xie Yong
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Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems [PDF]
, 2007 summary:We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The
Hiraoka, Yasuaki
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