Results 41 to 50 of about 8,908 (255)
The Homoclinic Orbits in the Liénard Plane
Journal of Mathematical Analysis and Applications, 1995 In reply to a question, posed by Roberto Conti, concerning the stability properties of the origin to a pseudolinear system in \(\mathbb{R}^ 2\), the situation is clarified for the well-known Liénard system. The notion of the maximal elliptic sector is shown to play an important role with respect to a zero solution to be a positive global (weak ...
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Homoclinic Orbits around Spinning Black Holes I: Exact Solution for the Kerr Separatrix
, 2008 Under the dissipative effects of gravitational radiation, black hole binaries will transition from an inspiral to a plunge. The separatrix between bound and plunging orbits features prominently in the transition.
G. Perez-Giz +7 more
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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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Homoclinic orbits of superlinear Hamiltonian systems [PDF]
Proceedings of the American Mathematical Society, 2011 In this paper, we consider the first-order Hamiltonian system \[ J u ˙ ( t ) + ∇ H ( t , u ( t ) ) = 0 , t ∈ R .
Guanwei Chen, Shiwang Ma
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On periodic solutions in the non-dissipative Lorenz model: the role of the nonlinear feedback loop
Tellus: Series A, Dynamic Meteorology and Oceanography, 2018 In this study, we discuss the role of the linear heating term and nonlinear terms associated with a non-linear feedback loop in the energy cycle of the three-dimensional (X–Y–Z) non-dissipative Lorenz model (3D-NLM), where (X, Y, Z) represent the ...
B.-W. Shen
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Shilnikov Homoclinic Bifurcation of Mixed-Mode Oscillations
, 2015 The Koper model is a three-dimensional vector field that was developed to study complex electrochemical oscillations arising in a diffusion process.
Guckenheimer, John, Lizarraga, Ian
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Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria
The Scientific World Journal, 2014 The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Fengjie Geng, Junfang Zhao
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Existence of homoclinic orbit for second-order nonlinear difference equation
Electronic Journal of Qualitative Theory of Differential Equations, 2010 By using the Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order nonlinear difference equation $\Delta \left[p(t)\Delta u(t-1)\right] +f(t,u(t))=0$ has at least one homoclinic orbit, where $t\in \mathbb{Z},\ u\in ...
Peng Chen, Li Xiao
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Solitary Waves and Homoclinic Orbits [PDF]
Annual Review of Fluid Mechanics, 1995 The notion that fluid motion often organizes itself into coherent structures has increasingly permeated modern fluid dynamics. Such localized objects appear in laminar flows and persist in turbulent states; from the water on windows on rainy days, to the circulations in planetary atmospheres. This review concerns solitary waves in fluids.
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Quantitative Biology, Volume 13, Issue 3, September 2025.Abstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Peng Zhang +3 more
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