Spiral Waves In Excitabe Media With Gradient Papameters

The study on spiral wave has been an important task of the pattern kinetics, which is subject to non-linear crossing subject. Spiral wave was observed in physics system, chemistry system, biology system: such as Ising-Block phase change in crystal, the aggregating slime-mold cell, the contraction of heart muscles, the CO oxidation on platinum surface, the chemical wave in reaction-diffusion media and so on.In the first chapter, we have a detailed theoretical annlysis on the formation and the dynamics behavior of spiral wave. We present several Partial differential equation model of spiral wave, and present a detailed introduction on the Canonical equation of the moving of spiral tips. In the second chapter, we give a brief introduction to the mechanism of the Instability and Broken of spiral wave. I the third chapter, we will have a deep see to the dynamic moving of spiral tips, that's our main work.Using a Barkley model as an example, we study spiral waves and spiral tips in a gradient excitable medium. The gradient distribution of parameters is introduced to depict the inhomogeneous medium. It is found that the parameter fluctuations play an important role in the morphology of spiral pattern and the movements of spiral tips. For a larger variance of the parameter fluctuations, the spiral waves are rough. For varied gradient parameters, it is observed that there exist three kinds of spiral behaviors, stable rotation, rebound of spiral tip from the boundary, and spiral disappear. A summary is made in the last chapter.