Abstract
It is well known that the spiral wave solution of the reaction‐diffusion equations is in the form of two qualitatively different classes of waves: rigidly rotating spirals or meandering spiral waves. The main objective of this paper is to study the stability of these waves. We develop an algorithm to deal with an operator dependent linearized system and to show that these waves are stable. This algorithm could be easily implemented. We also introduce a new approach for studying the dynamics change in the reaction diffusion system that obviates the need for tracing the path of spiral tip. Unlike tracing out the spiral tip which requires the intensive numerical procedures, our approach is easily implemented.
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