2003/07/31 by Chu-Pin Lo, Chu‐Pin Lo, Nedialko S. Nedialkov +4 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #37N25 #47N20 #47N60 #65G20 #65L05 #93A30 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #math.CA #math.DS #msc:37N25 #msc:47N20 #msc:47N60 #msc:65G20 #msc:65L05 #msc:93A30 #nlin.PS #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.math/0307394
arxiv created 2003/07/31 · openalex publication_date 2003/07/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Spiral waves arise in many biological, chemical, and physiological systems. The kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane. For this model, there appeared some results in the literature. However, these results all are based upon some simplification on the model or prior phenomenological assumptions on the solutions. In this paper, we use really full kinematic model to classify a generic kind of steadily rotating spiral waves, i.e., with positive (or negative) curvature. In fact, using our results (Theorem 8), we can answer the following questions: Is there any steadily rotating spiral wave for a given weakly excitable medium? If yes, what kind of information we can know about these spiral waves? e.g., the tip's curvature, the tip's tangential velocity, and the rotating frequency. Comparing our results with previous ones in the literature, there are some differences between them. There are only solutions with monotonous curvatures via simplified model but full model admits solutions with any given oscillating number of the curvatures.