Dissipative Solitons in Reaction Diffusion Systems: Mechanisms, Dynamics, Interaction
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Authors view affiliations Andreas W. Front Matter Pages i-xix. Pages Experimental Observations. Interaction of Slow Dissipative Solitudes. Dynamics and Interaction of Experimental Dissipative Solitons. This "Cited by" count includes citations to the following articles in Scholar.
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New citations to this author. New articles related to this author's research. Email address for updates. My profile My library Metrics Alerts. Sign in. Co-authors Andrey S. Hutchinson and J. Vanag and I.
Epstein, Localized patterns in reaction-diffusion systems ,, Chaos , 17 Yuan, T. Teramoto and Y.
Dissipative Solitons In Reaction Diffusion Systems Mechanisms Dynamics Interaction
Nishiura, Heterogeneity-induced defect bifurcation and pulse dynamics for a three-component reaction-diffusion system ,, Phys. E , 75 Zhabotinsky, M. Eager and I. Epstein, Refraction and reflection of chemical waves ,, Phys.
Instability of multi-spot patterns in shadow systems of reaction-diffusion equations. Matthieu Alfaro , Thomas Giletti. Varying the direction of propagation in reaction-diffusion equations in periodic media.
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Ming Mei. Stability of traveling wavefronts for time-delayed reaction-diffusion equations. Conference Publications , , Special : Masaharu Taniguchi. Multi-dimensional traveling fronts in bistable reaction-diffusion equations.
Traveling fronts in perturbed multistable reaction-diffusion equations. Henri Berestycki , Guillemette Chapuisat. Traveling fronts guided by the environment for reaction-diffusion equations. Theodore Kolokolnikov , Michael J.
Ward , Juncheng Wei. The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Zhaosheng Feng. Traveling waves to a reaction-diffusion equation. Stability of non-monotone non-critical traveling waves in discrete reaction-diffusion equations with time delay. Yicheng Jiang , Kaijun Zhang. Stability of traveling waves for nonlocal time-delayed reaction-diffusion equations. Multidimensional stability of time-periodic planar traveling fronts in bistable reaction-diffusion equations.
Global asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equations. Xiaojie Hou , Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Traveling wave solutions for time periodic reaction-diffusion systems. Instability of planar traveling waves in bistable reaction-diffusion systems. Traveling wave solutions of a reaction-diffusion predator-prey model. Traveling wave solutions in a nonlocal reaction-diffusion population model. Interface oscillations in reaction-diffusion systems above the Hopf bifurcation.
Piermarco Cannarsa , Giuseppe Da Prato. Invariance for stochastic reaction-diffusion equations. Martino Prizzi. A remark on reaction-diffusion equations in unbounded domains. American Institute of Mathematical Sciences. Previous Article Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis.
Traveling wave solutions of a 3-component reaction-diffusion model in smoldering combustion. Spatially localized patterns form a representative class of patterns in dissipative systems. We study how the dynamics of traveling spots in two-dimensional space change when heterogeneities are introduced in the media.
The simplest but fundamental one is a line heterogeneity of jump type.
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When spots encounter the jump, they display various outputs including penetration, rebound, and trapping depending on the incident angle and its height. The system loses translational symmetry by the heterogeneity, but at the same time, it causes the emergence of various types of heterogeneity-induced-ordered-patterns HIOPs replacing the homogeneous constant state.
We study these issues by using a three-component reaction-diffusion system with one activator and two inhibitors. The above outputs can be obtained through the interaction between the HIOPs and the traveling spots. The global bifurcation and eigenvalue behavior of HISPs are the key to understand the underlying mechanisms for the transitions among those dynamics.
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A reduction to a finite dimensional system is presented here to extract the model-independent nature of the dynamics. Selected numerical techniques for the bifurcation analysis are also provided. Keywords: bifurcation , heterogeneous media , Reaction-diffusion equations , traveling spot.
Heterogeneity-induced spot dynamics for a three-component reaction-diffusion system.