Antispiral waves in reaction-diffusion systems.

We report spontaneous antispiral wave formation in typical reaction-diffusion systems. Our findings qualitatively reproduce a series of phenomena recently observed in a Belousov-Zhabotinsky-type chemical reaction. We found that antispiral waves can occur only near the Hopf bifurcation, when the system is characterized by small amplitude oscillatory (as opposed to excitable) dynamics. For reaction-diffusion systems in the vicinity of the Hopf bifurcation, the specific conditions required for antispiral formation are established here through theoretical analyses and numerical simulations. Thus, this work provides a comprehensive description of the mechanisms underlying antispiral waves in reaction-diffusion systems.

[1]  R. J. Field,et al.  Oscillations and Traveling Waves in Chemical Systems , 1985 .

[2]  A. Winfree.  Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media. , 1991, Chaos.

[3]  R. M. Noyes,et al.  Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system , 1972 .

[4]  L. Kramer,et al.  Amplitude equations for description of chemical reaction–diffusion systems , 2000 .

[5]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[6]  J. Keener.  A geometrical theory for spiral waves in excitable media , 1986 .

[7]  José Jalife,et al.  Eikonal Relation in Highly Dispersive Excitable Media , 1997 .

[8]  J. Keener,et al.  Singular perturbation theory of traveling waves in excitable media (a review) , 1988 .

[9]  Vladimir K. Vanag,et al.  Pattern Formation in a Tunable Medium , 2001 .

[10]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[11]  Patrick S. Hagan,et al.  Spiral Waves in Reaction-Diffusion Equations , 1982 .

[12]  I. Epstein,et al.  Pattern formation in a tunable medium: the Belousov-Zhabotinsky reaction in an aerosol OT microemulsion. , 2001, Physical review letters.

[13]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[14]  P. G. Sørensen,et al.  Amplitude Equations and Chemical Reaction–Diffusion Systems , 1997 .

[15]  John Ross,et al.  Origin of spontaneous wave generation in an oscillatory chemical system , 1992 .

[16]  Irving R Epstein,et al.  Packet waves in a reaction-diffusion system. , 2002, Physical review letters.

[17]  W. Baxter,et al.  Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle. , 1993, Circulation research.

[18]  Biktasheva.  Drift of spiral waves in the complex ginzburg-landau equation due to media inhomogeneities , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  J. Tyson,et al.  Target patterns in a realistic model of the Belousov–Zhabotinskii reaction , 1980 .

[20]  Vladimir K. Vanag,et al.  Inwardly Rotating Spiral Waves in a Reaction-Diffusion System , 2001, Science.