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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BERNULLI DIFFERENTIAL EQUATION AND CHAOS
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2013 Existence conditions of homoclinic orbits for some systems of ordinary quadratic differential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic ...
V. Ye. Belozerov
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Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition
Abstract and Applied Analysis, 2012 We study the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems q¨−L(t)q+∇qW(t,q)=0, where L(t) is unnecessarily positive definite for all t∈ℝ, and ∇qW(t,q) is of at most linear growth and satisfies some twist condition ...
Qi Wang, Qingye Zhang
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Existence of homoclinic orbits for unbounded time-dependent $p$-Laplacian systems
Electronic Journal of Qualitative Theory of Differential Equations, 2016 In this paper, we consider the following ordinary $p$-Laplacian system \begin{equation} \frac{d}{dt}\big(|\dot u(t)|^{p-2}\dot u(t)\big)-\nabla K(t,u(t)) + \nabla W(t,u(t))=f(t),\tag{$HS$} \end{equation} where $t\in \mathbb{R}$ and $ p>1$.
Adel Daouas
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Normally Elliptic Singular Perturbations and Persistence of Homoclinic Orbits [PDF]
, 2010 Nan Lu, Chongchun Zeng
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A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem
Abstract and Applied Analysis, 2015 It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits.
Xuhua Cheng, Zhikun She
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The point charge oscillator: qualitative and analytical investigations
Mathematical Modelling and Analysis, 2019 We study the mathematical model of the point charge oscillator which has been derived by A. Beléndez et al. [2]. First we determine the global phase portrait of this model in the Poincaré disk.
Klaus R. Schneider
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Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors
Journal of Optimization, Differential Equations and Their ApplicationsNew types of neural ordinary differential equations (NODE) with power nonlinearities are considered. For these NODE systems, new conditions for the existence of homoclinic and heteroclinic orbits are found.
Vasiliy Ye. Belozyorov +2 more
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Perturbed Li–Yorke homoclinic chaos
Electronic Journal of Qualitative Theory of Differential Equations, 2018 It is rigorously proved that a Li–Yorke chaotic perturbation of a system with a homoclinic orbit creates chaos along each periodic trajectory. The structure of the chaos is investigated, and the existence of infinitely many almost periodic orbits out of ...
Marat Akhmet +3 more
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Homoclinic orbits for discrete Hamiltonian systems with subquadratic potential [PDF]
, 2013 Xiaoyan Lin, Xianhua Tang
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