Wave mediated synchronization of nonuniform oscillatory media.

We characterize the spatiotemporal evolution of a photosensitive Belousov-Zhabotinsky medium that is made up of coupled oscillatory cells with randomly distributed frequencies. The medium evolves from an initial state of multiple wave sources to a synchronized state governed by a single wave source. The synchronization occurs via a competition between the sources, which arises when the oscillators are not identical but have slightly different natural frequencies. The evolution of each cell is monitored to demonstrate frequency and phase synchronization of the inhomogeneous cellular medium, and a simple kinematic description for the advance of the phase-diffusion wave is presented.

[1]  L. Kuhnert,et al.  A new optical photochemical memory device in a light-sensitive chemical active medium , 1986, Nature.

[2]  W Wang,et al.  Clustering of arrays of chaotic chemical oscillators by feedback and forcing. , 2001, Physical review letters.

[3]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[4]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

[5]  A. S. Mikhailov,et al.  Multiple target pattern creation and synchronization phenomena , 1986 .

[6]  K. Showalter,et al.  Noise-supported travelling waves in sub-excitable media , 1998, Nature.

[7]  Milos Dolnik,et al.  Oscillatory cluster patterns in a homogeneous chemical system with global feedback , 2000, Nature.

[8]  E. Ott,et al.  EFFECT OF INHOMOGENEITY ON SPIRAL WAVE DYNAMICS , 1999 .

[9]  B. M. Fulk.  MATH , 1992 .

[10]  DeLiang Wang,et al.  Synchronization rates in classes of relaxation oscillators , 2004, IEEE Transactions on Neural Networks.

[11]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[12]  H. Jürgensen.  Synchronization , 2021, Inf. Comput..

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

[14]  Anna L. Lin,et al.  Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Alvin Shrier,et al.  Global organization of dynamics in oscillatory heterogeneous excitable media. , 2005, Physical review letters.

[16]  Monika Sharma,et al.  Chemical oscillations , 2006 .

[17]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[18]  R. Tönjes,et al.  Quasiregular concentric waves in heterogeneous lattices of coupled oscillators. , 2005, Physical review letters.

[19]  E. Ott,et al.  Spiral wave dynamics in oscillatory inhomogeneous media. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  L. Kuhnert,et al.  Analysis of the modified complete Oregonator accounting for oxygen sensitivity and photosensitivity of Belousov-Zhabotinskii systems , 1990 .

[21]  Jorge Flores,et al.  Model for Transition from Waves to Synchrony in the Olfactory Lobe of Limax , 2004, Journal of Computational Neuroscience.

[22]  G. Ermentrout,et al.  On chains of oscillators forced at one end , 1991 .