Study on the formation of chemical wave patterns for the Belousov-Zhabotinsky reaction system

The Belousov-Zhabotinsky (BZ) reaction system is famous because it can generate self-organized patterns, also known as "chemical waves". Pattern formation out of an initially homogeneous system is seemingly violating the 2nd-law of thermodynamics (order is produced out of disorder), while in fact, the BZ reaction is an open, far-from thermodynamic equilibrium system, where instability is the cause of morphogenesis and Hopf bifurcation of the reaction kinetics can generate self-oscillatory state trajectories. In this paper, the evolution of the BZ reaction in a two dimensional diffusion system is studied by the numerical computation methods, for the purpose of reconstructing the chemical wave patterns. The similarity of the chemical waves to many complex systems in biology, ecology and engineering makes current study potentially significant. With the study of the pattern formation, we hope provide some thoughts on complex system theory, thermodynamics of the self-oscillatory reaction system, and numerical computation methods on complex patterns, etc.