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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 ...
S. Malykh +4 more
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Cascades of Global Bifurcations and Chaos near a Homoclinic Flip Bifurcation: A Case Study [PDF]
SIAM Journal on Applied Dynamical Systems, 2018 We study a specific homoclinic bifurcation called a homoclinic flip bifurcation of case C, where a homoclinic orbit to a saddle equilibrium with real eigenvalues changes from being orientable to nonorientable.
Andrus Giraldo +2 more
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Homoclinic orbit and the violation of the chaos bound around a black hole with anisotropic matter fields [PDF]
Physical Review D, 2023 We study the homoclinic orbit and the violation of chaos bound, which are obtained by particle motions around a black hole that coexist with anisotropic matter fields.
S. Jeong +3 more
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Homoclinic orbits in Kerr-Newman black holes [PDF]
Physical Review D, 2023 We present the exact solutions of the homoclinic orbits for the timelike geodesics of the particle on the general nonequatorial orbits in the Kerr-Newman black holes. The homoclinic orbit is the separatrix between bound and plunging geodesics, a solution
Yi-Ting Li +3 more
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Hopf and homoclinic bifurcations for near-Hamiltonian systems
Journal of Differential Equations, 2017 Maoan Han, Yun Tian
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Bifurcation of big periodic orbits through symmetric homoclinics, application to Duffing equation [PDF]
Journal of Mahani Mathematical Research, 2023 We consider a planar symmetric vector field that undergoes a homoclinic bifurcation. In order to study the existence of exterior periodic solutions of the vector field around broken symmetric homoclinic orbits, we investigate the existence of fixed ...
Liela Soleimani, Omid RabieiMotlagh
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Sliding homoclinic bifurcations in a Lorenz-type system: Analytic proofs.
Chaos, 2021 Non-smooth systems can generate dynamics and bifurcations that are drastically different from their smooth counterparts. In this paper, we study such homoclinic bifurcations in a piecewise-smooth analytically tractable Lorenz-type system that was ...
V. Belykh, N. Barabash, I. Belykh
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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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Codimension 3 bifurcation from orbit-flip homoclinic orbit of weak type
Electronic Journal of Qualitative Theory of Differential Equations, 2015 This article is devoted to the research of a new codimension 3 homoclinic orbit bifurcation, which is the orbit-flip of weak type. Such kind of homoclinic orbit is a degenerate case of the orbit-flip homoclinic orbit.
Qiuying Lu, Guifeng Deng, Hua Luo
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Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity [PDF]
Communications in nonlinear science & numerical simulation, 2015 In this paper a Lorenz-like system, describing the process of rotating fluid convection, is considered. The present work demonstrates numerically that this system, also like the classical Lorenz system, possesses a homoclinic trajectory and a chaotic ...
G. Leonov, N. Kuznetsov, T. Mokaev
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