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Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…

Soft Condensed Matter · Physics 2016-05-02 Robert Großmann , Pawel Romanczuk , Markus Bär , Lutz Schimansky-Geier

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…

Biological Physics · Physics 2025-12-02 Antonio Matas-Gil , Robert G. Endres

Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…

Analysis of PDEs · Mathematics 2022-07-13 Arjen Doelman

Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…

Pattern Formation and Solitons · Physics 2026-02-05 Vinod Ramakrishnan , Michael J. Frazier

In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and…

Dynamical Systems · Mathematics 2024-12-24 Benjamin Aymard

Experiments with networks of discrete reactive bistable electrochemical elements organized in regular and nonregular tree networks are presented to confirm an alternative to the Turing mechanism for the formation of self-organized…

Pattern Formation and Solitons · Physics 2016-11-15 N. E. Kouvaris , M. Sebek , A. S. Mikhailov , I. Z. Kiss

Dynamical coherent structure (pattern) formation in the Klein-Gordon lattice excited by periodic external field near the optical resonance is studied. It is shown that besides spatial patterns discovered recently (V.M.Burlakov,…

patt-sol · Physics 2009-10-31 Victor M. Burlakov

We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state…

Statistical Mechanics · Physics 2009-11-07 J. Buceta , Katja Lindenberg , J. M. R. Parrondo

We study the evolution of a localized perturbation in a chemical system with multiple homogeneous steady states, in the presence of stirring by a fluid flow. Two distinct regimes are found as the rate of stirring is varied relative to the…

Chaotic Dynamics · Physics 2009-11-07 Zoltan Neufeld , Peter H. Haynes , Tamas Tel

We derive a necessary and sufficient condition for Turing instabilities to occur in two-component systems of reaction-diffusion equations with Neumann boundary conditions. We apply this condition to reaction-diffusion systems built from…

Mathematical Physics · Physics 2007-05-23 Rui Dilao

Spatiotemporal pattern formations in two-layer coupled reaction-diffusion Lengyel-Epstein system with distributed delayed couplings are investigated. Firstly, for the original decoupled system, it is proved that when the intra-reactor…

Analysis of PDEs · Mathematics 2024-12-23 Qidong Wu , Fengqi Yi

In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…

Pattern Formation and Solitons · Physics 2017-02-22 D. Hernández , E. C. Herrera-Hernández , M. Núñez-López , H. Hernández-Coronado

Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the…

Pattern Formation and Solitons · Physics 2021-06-21 Hatim Khudhair , Yanzhi Zhang , Nobuyuki Fukawa

The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…

Populations and Evolution · Quantitative Biology 2018-11-01 Lorenzo Contento , Masayasu Mimura

Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…

Pattern Formation and Solitons · Physics 2025-03-24 Juan F. Marín , Rafael Riveros Ávila , Saliya Coulibaly , Majid Taki , Mónica A. García-Ñustes

Crohn's disease is an inflammatory bowel disease (IBD) that is not well understood. In particular, unlike other IBDs, the inflamed parts of the intestine compromise deep layers of the tissue and are not continuous but separated and…

Analysis of PDEs · Mathematics 2020-07-28 Grégoire Nadin , Eric Ogier-Denis , Ana Isis Toledo , Hatem Zaag

In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…

Dynamical Systems · Mathematics 2018-01-11 Wakil Sarfaraz , Anotida Madzvamuse

We study the spatiotemporal properties of coherent states (peaks, holes, and fronts) in a bistable activator-inhibitor system that exhibits biochemical saturated autocatalysis, and in which fronts do not preserve spatial parity symmetry.…

Pattern Formation and Solitons · Physics 2008-03-20 Arik Yochelis , Alan Garfinkel

We study a reaction diffusion system of the activator-inhibitor type with inhomogeneous reaction terms showing spatiotemporal chaos. We analyze the topological properties of the unstable periodic orbits in the slow chaotic dynamics…

Statistical Mechanics · Physics 2009-11-10 S. Bouzat , H. s Wio , G. B. Mindlin

In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing…

Pattern Formation and Solitons · Physics 2014-02-20 Eleonora Tulumello , Maria Carmela Lombardo , Marco Sammartino