Results 51 to 60 of about 5,743 (240)

Pattern Formation and Nonlinear Waves Close to a 1:1 Resonant Turing and Turing–Hopf Instability

Studies in Applied Mathematics, Volume 155, Issue 5, November 2025.
ABSTRACT In this paper, we analyze the dynamics of a pattern‐forming system close to simultaneous Turing and Turing–Hopf instabilities, which have a 1:1 spatial resonance, that is, they have the same critical wave number. For this, we consider a system of coupled Swift–Hohenberg equations with dispersive terms and general, smooth nonlinearities.
Bastian Hilder, Christian Kuehn
wiley   +1 more source

Heteroclinic Orbits for Singular Hamiltonian Systems

Nelineinaya Dinamika
We are concerned with the existence of heteroclinic orbits for singular Hamiltonian systems of second order $\ddot{q}(t) + \nabla V(t, \,q)=0 $ where $V(t,\,q)$ is periodic in $t$ and has a singularity at a~point~${q=e}$. Suppose $V$ possesses a global maximum $\overline V$ on $\mathbb R \times \mathbb R ^N\setminus\{e\}$ and $V(t,\,x)= \overline{V ...
Antabli, Mohamed, Boughariou, Morched
openaire   +1 more source

Localization in inelastic rate dependent shearing deformations

, 2016
Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure.
Katsaounis, Theodoros, Lee, Min-Gi, Tzavaras, Athanasios   +2 more
core   +1 more source

The Existence of Moving Spike Patterns in an Attractive Chemotaxis Model

Mathematical Methods in the Applied Sciences, Volume 48, Issue 14, Page 13505-13516, 30 September 2025.
ABSTRACT We prove rigorously the existence of moving spike patterns in an attractive chemotaxis model with small diffusion coefficient for the chemical. In the zero diffusion limit, ϵ→0$$ \epsilon \to 0 $$, we prove that the non‐monotone traveling wave solutions of the system with ϵ>0$$ \epsilon >0 $$ converge to those of the system with ϵ=0$$ \epsilon
Tong Li, Casey Stone
wiley   +1 more source

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., Afraimovich V., Afraimovich V., ANDREY SHILNIKOV, Barrio R., Barrio R., Bykov V. V., Glendinning P., Gonchenko S. V., Hubner U., LEONID SHILNIKOV, Malkin M., ROBERTO BARRIO, Roshchin N., Rychlic M., Shilnikov A., Shilnikov L., Shilnikov L., Shilnikov L., Shilnikov L. P.   +19 more
core   +1 more source

Spiralling dynamics near heteroclinic networks [PDF]

, 2013
There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a {two parameter family of vector fields} on the three-dimensional sphere $\EU^3$, whose flow has a ...
Address Of Alex, Alexandre A. P. Rodrigues, Alexandre A. P. Rodrigues, Isabel, Isabel S. Labouriau, Isabel S. Labouriau, Re A. P. Rodrigues, S. Labouriau   +7 more
core   +1 more source

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

Analysis of Tangential Nonlinear Vibration on Machine Hydrostatic Slide

Shock and Vibration, 2019
In this paper, the nonlinear dynamic responses of the hydrostatic slide were investigated and the effects of damping and external force to control the vibration system were discussed.
Zhongkui Zhang, Feng Gao, Yan Li, Han Zhang   +3 more
doaj   +1 more source

Stability and bifurcations of heteroclinic cycles of type Z

, 2012
Dynamical systems that are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this paper we study stability properties of a class of structurally stable heteroclinic cycles in R^n which we ...
Podvigina, Olga
core   +1 more source

Nonlocal Cooperative Behavior, Psychological Effects, and Collective Decision‐Making: An Exemplification With Predator–Prey Models

Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12011-12037, August 2025.
ABSTRACT In bio‐social models, cooperative behavior has evolved as an adaptive strategy, playing multi‐functional roles. One of such roles in populations is to increase the success of the survival and reproduction of individuals and their families or social groups.
Sangeeta Saha, Swadesh Pal, Roderick Melnik   +2 more
wiley   +1 more source