Colliding Waves in a Model Excitable Medium: Preservation, Annihilation, and Bifurcation
نویسندگان
چکیده
We analyze the transition from annihilation to preservation of colliding waves. The analysis exploits the similarity between the local and global phase portraits of the system. The transition is shown to be the infinite-dimensional analog of the creation and annihilation of limit cycles in the plane via a homoclinic Andronov bifurcation, and has parallels to the nucleation theory of first-order phase transitions. [S0031-9007(97)04203-8]
منابع مشابه
Oscillatory Waves in an Inhomogeneous Excitable Medium
An excitable medium is a nonlinear dissipative dynamical system able to sustain undamped wave propagation. Examples of excitable media include cardiac tissue and neural media. This thesis investigates a class of novel dynamical phenomena in excitable media, known collectively as oscillatory waves. The examples of oscillatory waves considered here are Tango waves, breathers and pulse generators....
متن کاملSpiral Meandering
The complex, so called meandering, dynamics of spiral waves in excitable media is examined from the point of view of bifurcation theory. A computational bifurcation analysis is made of spiral dynamics. It is shown that spiral meandering is organized in parameter space around a codimension-two point where a Hopf bifurcation from rotating waves interacts with symmetries on the plane. A simple mod...
متن کاملTime-dependent wave selection for information processing in excitable media
We demonstrate an improved technique for implementing logic circuits in light-sensitive chemical excitable media. The technique makes use of the constant-speed propagation of waves along defined channels in an excitable medium based on the Belousov-Zhabotinsky reaction, along with the mutual annihilation of colliding waves. What distinguishes this work from previous work in this area is that re...
متن کاملHead-on collisions of waves in an excitable FitzHugh-Nagumo system: a transition from wave annihilation to classical wave behavior.
For the particular case of an excitable FitzHugh-Nagumo system with diffusion, we investigate the transition from annihilation to crossing of the waves in the head-on collision. The analysis exploits the similarity between the local and the global phase portraits of the system. We find that the transition has features typical of the nucleation theory of first-order phase transitions, and may be...
متن کاملAccumulations of T -points in a model for solitary pulses in an excitable reaction-diffusion medium
We consider a family of differential equations that describes traveling waves in a reaction diffusion equation modeling oxidation of carbon oxide on a platinum surface, near the onset of spatio-temporal chaos. The organizing bifurcation for the bifurcation structure with small carbon oxide pressures, turns out to be a codimension three bifurcation involving a homoclinic orbit to an equilibrium ...
متن کامل