Resonance Induced Pacemakers: A New Class of Organizing Centers for Wave Propagation in Excitable Media

Parmananda, P.; Mahara, Hitoshi; Amemiya, Takashi; Yamaguchi, Tomohiko

doi:10.1103/physrevlett.87.238302

Cited by 31 publications

(11 citation statements)

References 18 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Studding an excitable system under the action of external time-dependent perturbations is an actual problem of physics, neuroscience, physiology and medicine. Various periodic perturbations with periods comparable to the characteristic time scales of an excitable system [1][2][3][4][5][6], high-frequency (HF) perturbations [7][8][9][10], and a combination of low-and high-frequency perturbations [11,12] have been considered in the literature. In this paper we deal with the HF perturbations, which are of particular interest for the problems of neural control.…”

Section: Introductionmentioning

confidence: 99%

Pulse propagation and failure in the discrete FitzHugh-Nagumo model subject to high-frequency stimulation

Ratas

Pyragas

2012

Phys. Rev. E

View full text Add to dashboard Cite

We investigate the effect of a homogeneous high-frequency stimulation (HFS) on a one-dimensional chain of coupled excitable elements governed by the FitzHugh-Nagumo equations. We eliminate the high-frequency term by the method of averaging and show that the averaged dynamics depends on the parameter A=a/ω equal to the ratio of the amplitude a to the frequency ω of the stimulating signal, so that for large frequencies an appreciable effect from the HFS is attained only at sufficiently large amplitudes. The averaged equations are analyzed by an asymptotic theory based on the different time scales of the recovery and excitable variables. As a result, we obtain the main characteristics of a propagating pulse as functions of the parameter A and derive an analytical criterion for the propagation failure. We show that depending on the parameter A, the HFS can either enhance or suppress pulse propagation and reveal the mechanism underlying these effects. The theoretical results are confirmed by numerical simulations of the original system with and without noise.

show abstract

Section: Introductionmentioning

confidence: 99%

Pulse propagation and failure in the discrete FitzHugh-Nagumo model subject to high-frequency stimulation

Ratas

Pyragas

2012

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…Thus, the Oregonator model has been modified to include the photochemical generation of the inhibitor (Br À ) and the activator (HBrO 2 ), 20 and the extended modified Oregonator-class models have exhibited a variety of photoinduced behavior in homogeneous systems 21À23 and reaction-diffusion systems. 24 Petrov and co-workers have experimentally found the acceleration of a chemical wave under light irradiation. 25 These studies noticed ABSTRACT: The excitation of the photosensitive BelousovÀ Zhabotinsky (BZ) reaction induced by light stimulation was systematically investigated.…”

Section: ' Introductionmentioning

confidence: 99%

Photoexcited Chemical Wave in the Ruthenium-Catalyzed Belousov–Zhabotinsky Reaction

et al. 2011

Self Cite

View full text Add to dashboard Cite

The excitation of the photosensitive Belousov-Zhabotinsky (BZ) reaction induced by light stimulation was systematically investigated. A stepwise increase in the light intensity induced the excitation, whereas a stepwise decrease did not induce the excitation. The threshold values for the excitation were found to be a function of the initial and final light intensities, time variation in light intensity, and the concentration of NaBrO(3). The experimental results were qualitatively reproduced by a theoretical calculation based on a three-variable Oregonator model modified for the photosensitive BZ reaction. These results suggest that although the steady light irradiation is known to inhibit oscillation and chemical waves in the BZ system under almost all conditions, the stepwise increase in the light irradiation leads to the rapid production of an activator, resulting in the photoexcitation.

show abstract

“…Excitable systems in particular exhibit a novel coherence resonance phenomenon as a function of input noise level [3, 7]. Coherence resonance is displayed by a wide variety of systems such as different formulations of FitzHugh-Nagumo model [7–13], Belousov-Zhabotinsky reaction equations [14, 15], coupled Morris-Lecar models [16], and stochastic and chaotic systems [17, 18]. Experimental evidence of coherence resonance phenomenon is found in optical systems [19], electrochemical systems [20, 21], chaotic diode lasers [22], and semiconductor lasers [23].…”

Section: Introductionmentioning

confidence: 99%

Coherence resonance due to transient thresholds in excitable systems

Dodla

Wilson

2010

Phys. Rev. E

View full text Add to dashboard Cite

Excitable systems can have more than one response threshold, but accessing each of these is only facilitated by preferential choice of the appropriate components in the input noise. The coherence resonance phenomenon discovered by Pikovsky and Kurths [Phys. Rev. Lett. 78, 775 (1997)] utilizes only one response threshold, thus leaving the nature of the dynamics of a possible second threshold unspecified. Here we show using a FitzHugh-Nagumo excitable system that the second response threshold can be reached transiently by brief pulses in the negative noise component, leading to a coherence resonance phenomenon of its own. The resonance can occur both as a function of input amplitude and frequency. The phenomenon is also illustrated in more realistic Hodgkin-Huxley model equations, and analytical predictions are made using probabilistic considerations of the input. This phenomenon attributes more complex role noise can play in excitable systems.

show abstract

Resonance Induced Pacemakers: A New Class of Organizing Centers for Wave Propagation in Excitable Media

Cited by 31 publications

References 18 publications

Pulse propagation and failure in the discrete FitzHugh-Nagumo model subject to high-frequency stimulation

Pulse propagation and failure in the discrete FitzHugh-Nagumo model subject to high-frequency stimulation

Photoexcited Chemical Wave in the Ruthenium-Catalyzed Belousov–Zhabotinsky Reaction

Coherence resonance due to transient thresholds in excitable systems

Contact Info

Product

Resources

About