Results 101 to 110 of about 8,908 (255)
Analysis of the Stability and Chaotic Dynamics of an Ecological Model
Complexity, Volume 2024, Issue 1, 2024.Modelling has become an eminent tool in the study of ecological systems. Ecological modelling can help implement sustainable development, mathematical models, and system analysis that explain how ecological processes can promote the sustainable management of resources.
Muhammad Aqib Abbasi +6 more
wiley +1 more source
Ergodic measures with multi-zero Lyapunov exponents inside homoclinic classes
, 2016 We prove that for $C^1$ generic diffeomorphisms, if a homoclinic class $H(P)$ contains two hyperbolic periodic orbits of indices $i$ and $i+k$ respectively and $H(P)$ has no domination of index $j$ for any $j\in\{i+1,\cdots,i+k-1\}$, then there exists a ...
Wang, Xiaodong, Zhang, Jinhua
core
Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations
, 2013 In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations.
Choudhury, S. Roy +2 more
core +1 more source
Discrete Dynamics in Nature and Society, Volume 2024, Issue 1, 2024.In this paper, the limit cycles and local bifurcation of critical periods for a class of switching Z2 equivariant quartic system with two symmetric singularities are investigated. First, through the computation of Lyapunov constants, the conditions of the two singularities to become the centers are determined.
Jian Yang +3 more
wiley +1 more source
Nonintegrability of an extensible conducting rod in a uniform magnetic field
, 2011 The equilibrium equations for an isotropic Kirchhoff rod are known to be completely integrable. It is also known that neither the effects of extensibility and shearability nor the effects of a uniform magnetic field individually break integrability. Here
van der Heijden, G. H. M., Yagasaki, K.
core +1 more source
On Shilnikov's scenario in 3D: Topological chaos for vectorfields of class $C^1$
Electronic Journal of Qualitative Theory of Differential EquationsShilnikov's scenario in $\mathbb{R}^3$ means that the equation $x'=V(x)\in\mathbb{R}^3$ with $V(0)=0$ has a homoclinic solution and the eigenvalues of $DV(0)$ are $u>0$ and $\sigma\pm i\mu$ with ...
Hans-Otto Walther
doaj +1 more source
Homoclinic orbits in generalized Liénard systems
Journal of Mathematical Analysis and Applications, 2005 The author considers the planar Liénard-type system \[ \dot{x}=h(y)-F(x),\; \dot{y}=-g(x), \] where the functions \(F(x)\) and \(g(x)\) are continuous on an open interval \(I\) containing \(0\) and \(h(y)\) is continuous and strictly increasing on \(\mathbb{R}.\) Sufficient conditions are given, under which the system has a homoclinic orbit, i.e., a ...
openaire +3 more sources
Exploring the Influence of Oblateness on Asymptotic Orbits in the Hill Three-Body Problem
AppliedMathWe examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear ...
Vassilis S. Kalantonis
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Existence of homoclinic orbits for a class of nonlinear functional difference equations
Electronic Journal of Differential Equations, 2016 By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz ...
Xia Liu, Tao Zhou, Haiping Shi
doaj
, 2010 We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (it has
Crovisier, Sylvain, Pujals, Enrique R.
core +1 more source