Resonance clustering in globally coupled electrochemical oscillators with external forcing.

Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at frequency omega1) states; periodic forcing produces forced-entrained (omegaF) states. As a result of the interaction of mutual and forced entrainment, resonant cluster states occur with equal spacing of frequencies that have discretized frequencies following a resonance rule omegan congruent with nomega1-(n-1)omegaF. Resonance clustering requires an optimal, intermediate global coupling strength; at weak coupling the clusters have smaller sizes and do not strictly follow the resonance rule, while at strong coupling the population behaves similar to a single, giant oscillator.

[1]  I Fischer,et al.  Synchronization of delay-coupled oscillators: a study of semiconductor lasers. , 2005, Physical review letters.

[2]  Serhiy Yanchuk,et al.  Discretization of frequencies in delay coupled oscillators. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Vladimir Zykov,et al.  Control of spiral-wave dynamics in active media by periodic modulation of excitability , 1993, Nature.

[4]  K. Okuda.  Variety and generality of clustering in globally coupled oscillators , 1993 .

[5]  A. Winfree.  Biological rhythms and the behavior of populations of coupled oscillators. , 1967, Journal of theoretical biology.

[6]  E. Izhikevich,et al.  Thalamo-cortical interactions modeled by weakly connected oscillators: could the brain use FM radio principles? , 1998, Bio Systems.

[7]  John L. Hudson,et al.  Experiments on Arrays of Globally Coupled Periodic Electrochemical Oscillators , 1999 .

[8]  Hansel,et al.  Clustering in globally coupled phase oscillators. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[9]  S. Kai,et al.  Entrainment in a chemical oscillator chain with a pacemaker. , 2005, The journal of physical chemistry. A.

[10]  A. Mikhailov,et al.  Front reversals, wave traps, and twisted spirals in periodically forced oscillatory media. , 2006, Physical review letters.

[11]  M. Elowitz,et al.  Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[12]  J. L. Hudson,et al.  Emerging Coherence of Oscillating Chemical Reactions on Arrays: Experiments and Simulations , 2004 .

[13]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[14]  John L Hudson,et al.  Emerging Coherence in a Population of Chemical Oscillators , 2002, Science.

[15]  A. Zhabotinsky,et al.  Oscillatory clusters in the periodically illuminated, spatially extended Belousov-Zhabotinsky reaction. , 2001, Physical review letters.

[16]  Kenneth Showalter,et al.  Control of waves, patterns and turbulence in chemical systems , 2006 .

[17]  Valery Petrov,et al.  Resonant pattern formation in achemical system , 1997, Nature.

[18]  John L. Hudson,et al.  Extracting order parameters from global measurements with application to coupled electrochemical oscillators , 2004 .

[19]  Kaneko.  Chaotic but regular posi-nega switch among coded attractors by cluster-size variation. , 1989, Physical review letters.

[20]  Wataru Nakamura,et al.  Differential Response of Period 1 Expression within the Suprachiasmatic Nucleus , 2005, The Journal of Neuroscience.

[21]  A. Mikhailov,et al.  Standing Wave Patterns in the CO Oxidation Reaction on a Pt(110) Surface: Experiments and Modeling † , 2000 .

[22]  Hiroshi Kori,et al.  Slow switching in a population of delayed pulse-coupled oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[24]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[25]  J. Kurths,et al.  Synchronization of two interacting populations of oscillators. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Hakim,et al.  Dynamics of the globally coupled complex Ginzburg-Landau equation. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[27]  Kunihiko Kaneko,et al.  Life: An Introduction to Complex Systems Biology , 2006 .

[28]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[29]  A. Mikhailov,et al.  Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems , 2004 .

[30]  Moshe Sheintuch,et al.  Modeling periodic and chaotic dynamics in anodic nickel dissolution , 1992 .

[31]  J. L. Hudson,et al.  Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. , 2000, Chaos.

[32]  S. Reppert,et al.  Coordination of circadian timing in mammals , 2002, Nature.

[33]  S. Bernard,et al.  Spontaneous synchronization of coupled circadian oscillators. , 2005, Biophysical journal.

[34]  Kunihiko Kaneko,et al.  Complex Systems: Chaos and Beyond , 2001 .

[35]  Anna L. Lin,et al.  BLOCH-front turbulence in a periodically forced Belousov-Zhabotinsky reaction. , 2004, Physical review letters.

[36]  Hidetsugu Sakaguchi,et al.  Cooperative Phenomena in Coupled Oscillator Systems under External Fields , 1988 .

[37]  A. Mikhailov,et al.  Entrainment of randomly coupled oscillator networks by a pacemaker. , 2004, Physical review letters.

[38]  Carey,et al.  Resonant phase patterns in a reaction-diffusion system , 2000, Physical review letters.

[39]  Rae Silver,et al.  Orchestrating time: arrangements of the brain circadian clock , 2005, Trends in Neurosciences.

[40]  J. L. Hudson,et al.  Cooperative action of coherent groups in broadly heterogeneous populations of interacting chemical oscillators. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

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

[42]  A. Winfree.  The geometry of biological time , 1991 .