## 93 Citations

### Propagation and its failure in a lattice delayed differential equation with global interaction

- Mathematics
- 2005

### Pinning and propagation in spatially discrete bistable systems

- Mathematics
- 2016

Pinning and propagation failure results for wave fronts in bistable spatially discrete FitzHugh-Nagumo systems are established by means of a weak comparison principle. This comparison principle…

### Pushed and pulled fronts in a discrete reaction–diffusion equation

- Physics, Mathematics
- 2017

We consider the propagation of wave fronts connecting unstable and stable uniform solutions to a discrete reaction–diffusion equation on a one-dimensional integer lattice. The dependence of the…

### Wave Propagation in Discrete Media

- Physics, Mathematics
- 2005

We study wave front propagation in spatially discrete reaction-diffusion equations with cubic sources. Depending on the symmetry of the source, such wave fronts appear to be pinned or to glide at a…

### Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations

- Mathematics
- 2018

We survey some recent results on traveling waves and pattern formation in spatially discrete bistable reaction-diffusion equations. We start by recalling several classic results concerning the…

### Propagation failure of fronts in discrete inhomogeneous media with a sawtooth nonlinearity

- Mathematics
- 2016

Exact, steady-state, single-front solutions are constructed for a spatially discrete bistable equation with a piecewise linear reaction term, known as a sawtooth nonlinearity. These solutions are…

### Traveling Waves in One-Dimensional Excitable Media

- Physics
- 2014

Chapter 2 covers the classical problem of waves in one-dimensional excitable media, as exemplified by the FitzHugh–Nagumo model of action potential propagation along an axon. Standard methods for…

### Onset of wave fronts in a discrete bistable medium.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The transition from a standing front to a traveling front is studied in an array of symmetric bistable coupled oscillators in the context of a gluing bifurcation involving a pair of homoclinic loops.

### Traveling avalanche waves in spatially discrete bistable reaction – diffusion systems

- Mathematics
- 2003

Infinitely extended two-dimensional reaction–diffusion lattices composed of bistable cells are considered. A class of particular stable stationary solutions, called pattern solutions, is introduced…

### Traveling fronts in an array of coupled symmetric bistable units.

- PhysicsChaos
- 2003

Traveling fronts are shown to occur in an array of nearest-neighbor coupled symmetric bistable units and when the local dynamics is given by the Lorenz equations, the asymptotic behavior of the front velocity is found straightforwardly.

## References

SHOWING 1-10 OF 18 REFERENCES

### Reaction-diffusion processes in a one-dimensional array of active non-linear circuits

- Physics
- 1993

A linear array of coupled modified van der Pol oscillators has been studied both experimentally and numerically. A fixed width pulse was used to study the velocity of pulse-like travelling wave…

### Stability of traveling wavefronts for the discrete Nagumo equation

- Mathematics
- 1991

It has been shown that the discrete Nagumo equation \[ \dot u_n = d(u_{n - 1} - 2u_n + u_{n + 1} ) + f(u_n ),\quad n \in \mathbb{Z},\], has a traveling wavefront solution for sufficiently strong…

### Traveling Wave Solutions of Parabolic Systems

- Mathematics
- 1994

Part I. Stationary waves: Scalar equation Leray-Schauder degree Existence of waves Structure of the spectrum Stability and approach to a wave Part II. Bifurcation of waves: Bifurcation of…

### Propagation failure in arrays of coupled bistable chemical reactors

- Physics
- 1992

We consider a one-dimensional array of coupled stirred tank reactors. Each reactor operates with the bistable chlorite-iodide reaction. The reaction admits two stable steady sites (A and B). At time…

### Propagation and its failure in coupled systems of discrete excitable cells

- Physics
- 1987

We study propagation and its failure in systems of discrete coupled excitable cells. It is shown that propagation fails when coupling is weak, but succeeds if coupling is strong enough. We use a…

### Mechanisms for Nonuniform Propagation Along Excitable Cables

- PhysicsAnnals of the New York Academy of Sciences
- 1990

The authors' simulations with a discrete number of excitable cells, coupled by gap junctions, showed that the underlying mathematical structure of a saddle point threshold in an ionic model also contributes in an important way to creating a long delay.

### Mathematical Aspects of Reacting and Diffusing Systems

- Mathematics
- 1979

Preface and General Introduction.- 1. Modeling Considerations.- 1.1 Basic hypotheses.- 1.2 Redistribution processes.- 1.3 Boundaries and interfaces.- 1.4 Reactions with migration.- 1.5 The reaction…

### The effects of discrete gap junction coupling on propagation in myocardium.

- PhysicsJournal of theoretical biology
- 1991