Related papers: Traveling Waves in Bistable Reaction-Diffusion Cel…
This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…
The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between…
We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
An analysis of traveling wave solutions of partial differential equation (PDE) systems with cross-diffusion is presented. The systems under study fall in a general class of the classical Keller-Segel models to describe chemotaxis. The…
We present a method to control the position as a function of time of one-dimensional traveling wave solutions to reaction-diffusion systems according to a pre-specified protocol of motion. Given this protocol, the control function is found…
We study a family of reaction-diffusion equations that present a doubly nonlinear character given by a combination of the $p$-Laplacian and the porous medium operators. We consider the so-called slow diffusion regime, corresponding to a…
We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently…
Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is…
In this paper, we address the motion of charged particles subjected to a discrete spectrum of electrostatic waves. We focus on situations when transport dominates, leading to significant variations in particle velocity. Nonetheless, these…
For scalar reaction-diffusion equations, a traveling wave is a front which transforms a higher energy state to a lower energy state. The same is true for a system of equations with a gradient structure. At the core of this phenomenon, the…
Scientists have observed and studied diffusive waves in contexts as disparate as population genetics and cell signaling. Often, these waves are propagated by discrete entities or agents, such as individual cells in the case of cell…
Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. The motor exhibits distinct states of motility: active motion along filaments, and…
Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfv\'en waves are…
In this work, we present a computational analysis of the planar wave propagation behavior of a one-dimensional periodic multi-stable cellular material. Wave propagation in these materials is interesting because they combine the ability of…
We study the existence of monotone traveling wave solutions in a class of nonclassical diffusion equations that include both standard diffusion and a higher-order mixed space-time dispersive term. The reaction term is nonlinear and subject…