Spiral waves in excitable media due to noise and periodic forcing

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

[2]  S. Strogatz,et al.  Singular filaments organize chemical waves in three dimensions: I. Geometrically simple waves , 1983 .

[3]  V. Davydov,et al.  Observation of a helical-wave resonance in an excitable distributed medium , 1987 .

[4]  Marc Courtemanche,et al.  Stable three-dimensional action potential circulation in the FitzHugh-Nagumo model , 1990 .

[5]  Kenneth Showalter,et al.  Chemical waves in inhomogeneous excitable media , 1991 .

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

[7]  Electric-field-induced drift and deformation of spiral waves in an excitable medium. , 1992, Physical review letters.

[8]  INFLUENCE OF ELECTRIC-FIELD ON ROTATING SPIRAL WAVES IN THE BELOUSOV-ZHABOTINSKY REACTION , 1992 .

[9]  B Hess,et al.  Phototaxis of Spiral Waves , 1992, Science.

[10]  Pérez-Muñuzuri,et al.  Mechanism of the electric-field-induced vortex drift in excitable media. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Harm Hinrich Rotermund,et al.  Reaction diffusion patterns in the catalytic CO‐oxidation on Pt(110): Front propagation and spiral waves , 1993 .

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

[13]  H. Engel,et al.  Compound rotation of spiral waves in active media with periodically modulated excitability , 1993 .

[14]  C F Starmer,et al.  Vulnerability in an excitable medium: analytical and numerical studies of initiating unidirectional propagation. , 1993, Biophysical journal.

[15]  M. Eiswirth,et al.  Turbulence due to spiral breakup in a continuous excitable medium. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[17]  Frisch,et al.  Spiral waves in liquid crystal. , 1994, Physical review letters.

[18]  C. Frank Starmer,et al.  Vulnerability in one-dimensional excitable media , 1994 .

[19]  H. Engel,et al.  Chemical turbulence and standing waves in a surface reaction model: The influence of global coupling and wave instabilities. , 1994, Chaos.

[20]  Krinsky,et al.  Elastic excitable medium. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  O. Steinbock,et al.  External forcing of spiral waves. , 1994, Chaos.

[22]  Jung,et al.  Spatiotemporal stochastic resonance in excitable media. , 1995, Physical review letters.

[23]  Gottfried Mayer-Kress,et al.  Noise controlled spiral growth in excitable media. , 1995, Chaos.

[24]  Aliev,et al.  Multiple responses at the boundaries of the vulnerable window in the Belousov-Zhabotinsky reaction. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Marc Courtemanche,et al.  Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity. , 1996, Chaos.

[26]  Q. Ouyang,et al.  Transition from spirals to defect turbulence driven by a convective instability , 1996, Nature.

[27]  P. Hogeweg,et al.  Spatial pattern formation during aggregation of the slime mould Dictyostelium discoideum. , 1996, Journal of theoretical biology.

[28]  Andrew Belmonte,et al.  Spiral instability to line sources in forced chemical pattern turbulence , 1996 .

[29]  P. Jung,et al.  Thermal Waves, Criticality, and Self-Organization in Excitable Media , 1997 .

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

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

[32]  F Moss,et al.  Noise-induced spiral waves in astrocyte syncytia show evidence of self-organized criticality. , 1998, Journal of neurophysiology.

[33]  Lutz Schimansky-Geier,et al.  Noise-Sustained Pulsating Patterns and Global Oscillations in Subexcitable Media , 1999 .

[34]  Lutz Schimansky-Geier,et al.  Noise-induced spiral dynamics in excitable media , 1999 .

[35]  Kenneth Showalter,et al.  Noise Driven Avalanche Behavior in Subexcitable Media , 1999 .

[36]  Xie,et al.  Eliminating spatiotemporal chaos and spiral waves by weak spatial perturbations , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  Zhou,et al.  Experimental studies on long-wavelength instability and spiral breakup in a reaction-diffusion system , 2000, Physical review letters.

[38]  Casademunt,et al.  Brownian motion of spiral waves driven by spatiotemporal structured noise , 2000, Physical review letters.

[39]  Q Ouyang,et al.  Transition from spirals to defect-mediated turbulence driven by a doppler instability. , 2000, Physical review letters.

[40]  Alexander S. Mikhailov,et al.  Controlling Chemical Turbulence by Global Delayed Feedback: Pattern Formation in Catalytic CO Oxidation on Pt(110) , 2001, Science.

[41]  Elimination of spiral chaos by periodic force for the Aliev-Panfilov model. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[43]  Harald Engel,et al.  Feedback-mediated control of spiral waves , 2004 .

[44]  M. Perc.  Spatial coherence resonance in excitable media. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  M. Perc.  Spatial decoherence induced by small-world connectivity in excitable media , 2005 .

[46]  Matjaž Perc,et al.  Persistency of noise-induced spatial periodicity in excitable media , 2005 .

[47]  Guoyong Yuan,et al.  Control of spiral waves and spatiotemporal chaos by periodic perturbation near the boundary , 2005 .

[48]  Gang Hu,et al.  Suppress Winfree turbulence by local forcing excitable systems. , 2005, Physical review letters.

[49]  J. Lamb,et al.  Hopf bifurcation from relative periodic solutions; secondary bifurcations from meandering spirals , 2006 .

[50]  Matjaz Perc,et al.  Minimal model for spatial coherence resonance. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  J. M. Sancho,et al.  Spatiotemporal order out of noise , 2007 .

[52]  Matjaž Perc,et al.  Spatial coherence resonance in neuronal media with discrete local dynamics , 2007 .

[53]  Eliminating spiral waves and spatiotemporal chaos using feedback signal , 2007 .

[54]  M. Perc.  Stochastic resonance on excitable small-world networks via a pacemaker. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  Matjaž Perc,et al.  Effects of small-world connectivity on noise-induced temporal and spatial order in neural media , 2007 .

[56]  Chunni Wang,et al.  Suppression of spiral waves in light-sensitive media using chaotic signal modulated scheme , 2007 .

[57]  Z. Duan,et al.  Delay-enhanced coherence of spiral waves in noisy Hodgkin–Huxley neuronal networks , 2008 .

[58]  Control spiral and multi-spiral wave in the complex Ginzburg–Landau equation , 2008 .

[59]  Matjaz Perc,et al.  Emergence of target waves in paced populations of cyclically competing species , 2009, 0908.0563.

[60]  Matjaž Perc,et al.  Pacemaker-guided noise-induced spatial periodicity in excitable media , 2009 .

[61]  A. Xu,et al.  Control of spiral-wave dynamics using feedback signals from line detectors , 2010, 1004.0045.

[62]  Jun Ma,et al.  COLLECTIVE BEHAVIORS OF SPIRAL WAVES IN THE NETWORKS OF HODGKIN-HUXLEY NEURONS IN PRESENCE OF CHANNEL NOISE , 2010 .

[63]  Ya Jia,et al.  Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons , 2010 .