Results 21 to 30 of about 5,743 (240)
HETEROCLINIC ORBITS ARISING FROM COUPLED CHUA'S CIRCUITS [PDF]
International Journal of Bifurcation and Chaos, 2003 In this paper, we study the existence of heteroclinic orbits for ordinary differential equations which arise from a one-dimensional array of Chua's circuits. By using the upper and lower solutions method, and a zero-order approximation we show that for a certain set of parameters there exist traveling wave solutions for some given wave speeds.
Chan, Whei-Ching C., Shi, Shaoyun
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On the Melnikov function [PDF]
ریاضی و جامعه, 2023 In this article, we have tried to introduce one of the most important topics in the subject of dynamical systems, namely the Melnikov function, in simple language.
Majid Karimi Amaleh
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Quasiperiodic, periodic, and slowing-down states of coupled heteroclinic cycles [PDF]
, 2012 We investigate two coupled oscillators, each of which shows an attracting heteroclinic cycle in the absence of coupling. The two heteroclinic cycles are nonidentical. Weak coupling can lead to the elimination of the slowing-down state that asymptotically
Cross, M. C. +3 more
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Heteroclinic Orbits of Semilinear Parabolic Equations
Journal of Differential Equations, 1996 The authors study attractors of semilinear parabolic problems \[ u_t= u_{xx}+ f(x, u, u_x),\;t> 0,\;0< x< 1,\quad u_x(t, 0)= u_x(t, 1)= 0. \] Here \(f\in C^2\) and appropriate dissipativity conditions are assumed so that the global attractor exists. It is known that the attractor consists of equilibria and heteroclinic orbits connecting them.
Fiedler, Bernold, Rocha, Carlos
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International Journal of Mechanical System Dynamics, 2023 Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems. In this paper, a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an ...
Yong Huang
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Mathematics, 2023 In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave ...
Mengke Yu, Cailiang Chen, Qiuyan Zhang
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Low-Thrust Lyapunov to Lyapunov and Halo to Halo with $L^2$-Minimization [PDF]
, 2016 In this work, we develop a new method to design energy minimum low-thrust missions (L2-minimization). In the Circular Restricted Three Body Problem, the knowledge of invariant manifolds helps us initialize an indirect method solving a transfer mission ...
Chupin, Maxime +2 more
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Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues
The Scientific World Journal, 2014 By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the ...
Yinlai Jin +5 more
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Existence of traveling waves in a delayed convecting shallow water fluid model
Electronic Research Archive, 2023 This paper investigates a delayed shallow water fluid model that has not been studied in previous literature. Applying geometric singular perturbation theory, we prove the existence of traveling wave solutions for the model with a nonlocal weak delay ...
Minzhi Wei
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Dynamics of a plant-herbivore model with a chemically-mediated numerical response
Mathematics in Applied Sciences and Engineering, 2021 A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modified numerical response.
Lin Wang, James Watmough, Fang Yu
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