Related papers: Traveling waves in a mean field learning model
A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and…
We analyze the weak solution concept for the Fornberg-Whitham equation in case of traveling waves with a piecewise smooth profile function. The existence of discontinuous weak traveling wave solutions is shown by means of analysis of a…
The Fitzhugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing to better understand the essential dynamics of the interaction of the membrane potential and the restoring force and to capture,…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
We construct the traveling wave solutions of an FKPP growth process of two densities of particles, and prove that the critical traveling waves are locally stable in a space where the perturbations can grow exponentially at the back of the…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
This paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…
This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory…
The complex formations exhibited by schooling fish have long been the object of fascination for biologists and physicists. However, the physical and sensory mechanisms leading to organized collective behavior remain elusive. On the physical…
Single-species reaction-diffusion equations, such as the Fisher-KPP and Porous-Fisher equations, support travelling wave solutions that are often interpreted as simple mathematical models of biological invasion. Such travelling wave…
We study dispersive models of fluid flow in viscoelastic vessels, derived in the study of blood flow. The unknowns in the models are the velocity of the fluid in the axial direction and the displacement of the vessel wall from rest. We…
Power systems usually go through electromagnetic and electromechanical transient processes after different disturbances. Learning the characteristics and the differences between them are important but not easy for students majoring in power…
This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories…
The development of macroscopic descriptions for the joint dynamics and behavior of large heterogeneous ensembles subject to ecological forces like dispersal remains a central challenge for mathematicians and biological scientists alike.…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
An essential part of nondestructive testing and experimental modeling of waveguides is the decomposition of propagating wave patterns. The traveling wave ratio is a measure of partial reflections assisting in quantifying the pureness of a…
Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are…
In this paper we study the existence of traveling wave solutions for a free-boundary problem modeling the phase transition of a material where the heat is transported by both conduction and radiation. Specifically, we consider a…