Generalized complex anisotropy expression in excitable mediaZhi Zhu He1 and Jing Liu1, 2
1 Technical Institute of Physics and Chemistry, Chinese Academy of Sciences - P. O. Box 2711, Beijing 100190, China
2 Biomedical Engineering Department, School of Medicine, Tsinghua University - Beijing 100084, China
received 4 August 2008; accepted in final form 24 November 2008; published January 2009
published online 12 January 2009
In this letter, a complex expression is constructed to characterize the reaction diffusion phenomena in anisotropic excitable media. The theoretical model thus established has general significance and can effectively capture the basic properties of chemical-wave propagation in the real-world media. Particularly, an eikonal relation is derived to account for the effects of complex anisotropy. It indicates that a sufficiently strong complex anisotropy can lead to chemical-wave propagation instabilities such as the occurrences of shocks on the propagating wavefront. The correlation can also predict how the particular form of anisotropy induces complex pattern formation such as “polygon-shaped” patterns. Numerical simulations on a two-dimensional system with complex anisotropy sustain these analysis results.
82.40.Bj - Oscillations, chaos, and bifurcations.
05.45.-a - Nonlinear dynamics and chaos.
82.40.Ck - Pattern formation in reactions with diffusion, flow and heat transfer.
© EPLA 2009