Results 71 to 80 of about 8,908 (255)
Journal of Applied Mathematics, 2012 The authors study the existence and uniqueness of a set with 2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a ...
Lijuan Chen, Shiping Lu
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Measure-Expansive Homoclinic Classes for C1 Generic Flows
Mathematics, 2020 In this paper, we prove that for a generically C1 vector field X of a compact smooth manifold M, if a homoclinic class H(γ,X) which contains a hyperbolic closed orbit γ is measure expansive for X then H(γ,X) is hyperbolic.
Manseob Lee
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Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.The first‐ and second‐order wave equations of Benjamin–Ono control the propagation of nonlinear Rossby waves in a rotating fluid and define a broad class of internal waves in a stratified fluid of enormous depth. New solitary wave solutions and the modulation instability of the solutions for the first‐ and second‐order Benjamin–Ono partial differential
Wilson Osafo Apeanti +3 more
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Journal of Biological Dynamics, 2020 In this paper, Melnikov analysis of chaos in a simple SIR model with periodically or stochastically modulated nonlinear incidence rate and the effect of periodic and bounded noise on the chaotic motion of SIR model possessing homoclinic orbits are ...
Yanxiang Shi
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Reduced and bifurcation analysis of intrinsically bursting neuron model
Electronic Research Archive, 2023 Intrinsic bursting neurons represent a common neuronal type that displays bursting patterns upon depolarization stimulation. These neurons can be described by a system of seven-dimensional equations, which pose a challenge for dynamical analysis.
Bo Lu, Xiaofang Jiang
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New Solutions of Breaking Soliton Equation Using Softmax Method
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.This study presents the application of a novel Softmax method to obtain exact analytical solutions of the breaking soliton equation, a nonlinear partial differential equation that models complex wave phenomena. By transforming the governing equation into an ordinary differential equation using a traveling wave transformation and constructing a solution
Nguyen Minh Tuan +3 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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Journal of Mathematics, Volume 2025, Issue 1, 2025.This research describes a predator–prey system that takes into account the generalized Allee effect, aiming to derive general conclusions applicable to specific Allee effect functions through the use of a generalized function. To make sure the suggested model was accurate from a mathematical perspective, we first investigated the solutions to determine
Gaji Zhuo +5 more
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Structurally Stable Homoclinic Classes [PDF]
, 2014 In this paper we study structurally stable homoclinic classes. In a natural way, the structural stability for an individual homoclinic class is defined through the continuation of periodic points.
Wen, Xiao
core
Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial
, 2012 A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor.
Abad A. +19 more
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