Results 21 to 30 of about 2,258 (187)
From degenerate heteroclinic loop to transverse homoclinic points
Changrong Zhu
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Advances in Mathematical Physics, Volume 2022, Issue 1, 2022., 2022 The main idea of this paper is to investigate the exact solutions and dynamic properties of a space‐time fractional perturbed nonlinear Schrödinger equation involving Kerr law nonlinearity with conformable fractional derivatives. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is ...
Shuxin Bao, Shuangqing Chen, Ming Mei
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Self‐Excited and Hidden Chaotic Attractors in Matouk’s Hyperchaotic Systems
Discrete Dynamics in Nature and Society, Volume 2022, Issue 1, 2022., 2022 Self-excited and hidden chaotic attractors are interesting complex dynamical phenomena. Here, Matouk’s hyperchaotic systems are shown to have self-excited and hidden chaotic attractors, respectively. Two case studies of hidden chaotic attractors are provided which are examined with orders 3.08 and 3.992, respectively.
A. Othman Almatroud +5 more
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Boundary Value Problems for Liénard‐Type Equations with Quadratic Dependence on the “Velocity”
Abstract and Applied Analysis, Volume 2022, Issue 1, 2022., 2022 The estimates were obtained for the number of solutions for the Neumann and Dirichlet boundary value problems associated with the Liénard equation with a quadratic dependence on the “velocity.” Sabatini’s transformation is used to reduce this equation to a conservative one, which does not contain the derivative of an unknown function.
A. Kirichuka, F. Sadyrbaev, Paul Eloe
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Nine Limit Cycles in a 5-Degree Polynomials Liénard System
Complexity, 2020 In this article, we study the limit cycles in a generalized 5-degree Liénard system. The undamped system has a polycycle composed of a homoclinic loop and a heteroclinic loop.
Junning Cai, Minzhi Wei, Hongying Zhu
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Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling [PDF]
, 2001 The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the formation of a ...
A.T. Winfree +18 more
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Self‐Propulsion and Shear Flow Align Active Particles in Nozzles and Channels
Advanced Intelligent Systems, Volume 3, Issue 2, February 2021., 2021 Chemically self‐propelled gold–platinum nanorods show rapid alignment flow and migration against the flow when flown through micro‐channels and nozzles. The flow shear rate determines the tilting angle with respect to the bottom, making particles reorient like a weather vane.
Leonardo Dominguez Rubio +5 more
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Dense heteroclinic tangencies near a Bykov cycle [PDF]
, 2014 This article presents a mechanism for the coexistence of hyperbolic and non-hyperbolic dynamics arising in a neighbourhood of a Bykov cycle where trajectories turn in opposite directions near the two nodes --- we say that the nodes have different ...
Labouriau, Isabel S. +1 more
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Existence of Solitary Waves in a Perturbed KdV‐mKdV Equation
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this paper, we establish the existence of a solitary wave in a KdV‐mKdV equation with dissipative perturbation by applying the geometric singular perturbation technique and Melnikov function. The distance of the stable manifold and unstable manifold is computed to show the existence of the homoclinic loop for the related ordinary differential ...
Chengqun Li +3 more
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Some results on homoclinic and heteroclinic connections in planar systems [PDF]
, 2009 Consider a family of planar systems depending on two parameters $(n,b)$ and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when $\Phi(n,b)=0.$ We present a method that allows to ...
Andronov A A +12 more
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