This article concerns the bistable traveling wavefronts of a nonlocal dispersal equation with convolution type bistable nonlinearity. Applying a homotopy method, we establish the existence of traveling wavefronts. If the wave speed does not vanish, i.e. c 6= 0, then the uniqueness (up to translation) and the globally asymptotical stability of traveling wavefronts are proved by the comparison pr...

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In many problems, e.g., in combustion or solidification, one observes traveling waves that propagate with constant velocity and shape in the x direction, say, are independent of y and z and describe transitions between two equilibrium states, e.g., the burned and the unburned reactants. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves havi...

regarding the importance of competitive advantages among the transportation systems, improving the costumer’s satisfaction is an important factor in attracting them to these systems. in this research, we focus on the effects of constructing new stations on users and a new mathematical model is proposed for this problem. in the proposed model, two simultaneous effects on customers by constructin...

We study the existence of traveling waves in a one-dimensional network of integrateand-fire neurons with finite support coupling. We show that when the reset after spiking is sufficiently low, the interspike intervals (ISIs) for a traveling wave with an explicit first wave front can be computed. Further, we analytically derive a self-consistency equation that generates an explicit dispersion re...

This paper extends some of the previous work on synaptically generated traveling waves from one dimension to two dimensions. Numerical simulations of networks of the so-called theta neurons were used for exploration of the existence, stability and the nature of these waves. The symmetric nature of the traveling waves was justi"ed and a numerical scheme for evaluating the velocity of the traveli...

We study the existence of traveling waves in a one-dimensional network of integrate-and-#re neurons with #nite support coupling. We show that when the reset after spiking is su2ciently low, the interspike intervals (ISIs) for a traveling wave with an explicit #rst wave front can be computed. Further, we analytically derive a self-consistency equation that generates an explicit dispersion relati...

We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions connecting an unstable equilibrium to the closest stable equilibrium for all speeds exceeding a critical value. We show that these are, in fact, the only trav...

This paper is concerned with the traveling waves for a class of delayed non-local diffusion equations with crossing-monostability. Based on constructing two associated auxiliary delayed non-local diffusion equations with quasi-monotonicity and a profile set in a suitable Banach space using the traveling wave fronts of the auxiliary equations, the existence of traveling waves is proved by Schaud...

The Symmetric Traveling Salesman Polytope Sn for a fixed number n of cities is a face of the corresponding Graphical Traveling Salesman Polyhedron Pn. This has been used to study facets of Sn using Pn as a tool. In this paper, we study the operation of “rotating” (or “lifting”) valid inequalities for Sn to obtain a valid inequalities for Pn. As an application, we describe a surprising relations...