Results 41 to 50 of about 1,641 (211)
Homoclinic orbits for an unbounded superquadratic [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2010 We consider the following nonperiodic diffusion systems $$ \left\{\begin{array}{ll} \partial_{t}u-\triangle_{x}u+b(t,x)\nabla_{x}u+V(x)u=G_{v} (t,x,u,v), \\ -\partial_{t}v-\triangle_{x}v-b(t,x)\nabla_{x}v+V(x)v=G_{u} (t,x,u,v), \end{array}\right.
Junxiang Xu +3 more
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Closed geodesics and the first Betti number
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We prove that, on any closed manifold of dimension at least two with non‐zero first Betti number, a C∞$C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this existence result combining a theorem of Mañé together with the following new theorem of ...
Gonzalo Contreras, Marco Mazzucchelli
wiley +1 more source
Revealing asymmetric homoclinic and heteroclinic orbits
Electronic Research ArchiveAlthough scholars have proven the existence of a pair of homoclinic orbits to the origin, or a pair of heteroclinic orbits to the origin along with a pair of nontrivial equilibria in symmetric Lorenz, Chen, and Lü systems, they have rarely dealt with ...
Jun Pan, Haijun Wang, Feiyu Hu
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Protected Chaos in a Topological Lattice
Advanced Science, Volume 12, Issue 28, July 24, 2025.Topological and chaotic dynamics are often considered incompatible, with one expected to dominate or disrupt the other. This work reveals that topological localization can persist even under strong chaotic dynamics and, counter‐intuitively, protect chaotic behavior.
Haydar Sahin +6 more
wiley +1 more source
Numerical Simulation of Mixing Enhancement in a Single Screw Extruder by Different Internal Baffles
Macromolecular Theory and Simulations, Volume 34, Issue 4, July 2025.Three rows of plate baffles and plow‐shaped baffles are employed to introduce chaos into the flow channel of a single screw extruder. Mixing is numerically characterized in terms of the evolution of tracer particles, Poincaré sections, shear rates, mixing index, distribution probability function of mixing index, and their integral functions.
Huiwen Yu +4 more
wiley +1 more source
Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions
Abstract and Applied Analysis, 2013 By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.
Qi Wang, Qingye Zhang
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Homoclinic Orbits in Slowly Varying Oscillators
SIAM Journal on Mathematical Analysis, 1987 Perturbed Hamiltonian systems of the type \(\dot x=f(x)+\epsilon g(x,t,\lambda)\) are considered, where \(f: {\mathbb{R}}^ 3\to {\mathbb{R}}^ 2\), \(g: {\mathbb{R}}^{4+k}\to {\mathbb{R}}^ 3\) are sufficiently smooth, g(x,t,\(\lambda)\) is periodic in t, \(\lambda\) is a k-vector parameter, and \(\epsilon\) is a small positive parameter.
Wiggins, Stephen, Holmes, Philip
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Studies in Applied Mathematics, Volume 155, Issue 1, July 2025.ABSTRACT This work aims to study some dynamical aspects of the nonlinear logarithmic Schrödinger equation (NLS‐log) on a tadpole graph, namely, a graph consisting of a circle with a half‐line attached at a single vertex. By considering Neumann–Kirchhoff boundary conditions at the junction, we show the existence and the orbital stability of standing ...
Jaime Angulo Pava +1 more
wiley +1 more source
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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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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