Stabilization of spiral wave and turbulence in the excitable media using parameter perturbation scheme

This paper proposes a scheme of parameter perturbation to suppress the stable rotating spiral wave, meandering spiral wave and turbulence in the excitable media, which is described by the modified Fitzhug-Nagumo （MFHN） model. The controllable parameter in the MFHN model is perturbed with a weak pulse and the pulse period is decided by the rotating period of the spiral wave approximatively. It is confirmed that the spiral wave and spiral turbulence can be suppressed greatly. Drift and instability of spiral wave can be observed in the numerical simulation tests before the whole media become homogeneous finally.

Suppression of spiral waves using intermittent local electric shock

In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock （about 0.4 to 0.7） imposed on a random selected n × n grids （n =1 - 5, compared with the original 256×256 lattice） and monitored synchronically the evolutions of the activator on the grids as the sampled signal of the activator steps out a given threshold （i.e., the electric shock works on the n ~ n grids if the activator u ≤ 0.4 or u ≥ 0.8）. The numerical simulations show that a breakup of spiral is observed in the media state evolution to finally obtain homogeneous states if the electric shock with appropriate intensity is imposed.

Development and transition of spiral wave in the coupled Hindmarsh-Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh-Rose （H-R） neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D＇, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons （or sites） and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.

Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

We numerically study the dynamics of spiral waves in the excitable system with the excitability modulated by a rectangle wave. The tip trajectories and their variations with the modulation period T are explained by the corre- sponding spectrum analysis. For a large T, the external modulation leads to the occurrence of more frequency peaks and these frequencies change with the modulation period according to their specific rules, respectively. Some of the frequencies and a primary frequency fl determine the corresponding curvature periods, which are locked into rational multiplies of the modulation period. These frequency-locking behaviours and the limited life-span of the frequencies in their variations with the modulation period constitute many resonant entrainment bands in the T axis. In the main bands, which follow the relation T/T12 = m/n, the size variable Rx of the tip trajectory is a monotonic increasing function of T. The rest of the frequencies are linear combinations of the two ones. Due to the complex dynamics, many unique tip trajectories appear at some certain T. We find also that spiral waves are eliminated when T is chosen from the end of the main resonant bands. This offers a useful method of controling the spiral wave.

Synchronization of spiral waves in a two-layer coupled inhomogeneous excitable system

We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.

Size transition of spiral waves using the pulse array method

The domain size of spiral waves is an important issue in studies of two-dimensional （2D） spatiotemporal patterns. In this work, we use the 2D complex Ginzburg-Landau equation （CGLE） as our model and find that an initially big spiral can successfully transfer to several small spirals by applying a pulse array method. The impacts of several important factors, such as array density, controlling intensity and pulsing time, are investigated. This control approach may be useful for the control of 2D spatiotemporal patterns and has potential applications in the control of some realistic systems, such as meteorological and cardiac systems.

Spiral Waves and Multiple Spatial Coherence Resonances Induced by Colored Noise in Neuronal Network

Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network.

Controlling spiral wave with target wave in oscillatory systems

Spiral waves have been controlled by generating target waves with a localized inhomogeneity in the oscillatory medium. The competition between the spiral waves and target waves is discussed. The effect of the localized inhomogeneity size has also been studied.

Instability and Death of Spiral Wave in a Two-Dimensional Array of Hindmarsh-Rose Neurons

Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriateparameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventriculartachycardia that can denervate into polymorphic tachycardia and ventricular fibrillation. The neuronal system oftenconsists of a large number of neurons with complex connections. In this paper, we theoretically study the transitionfrom spiral wave to spiral turbulence and homogeneous state (death of spiral wave) in two-dimensional array of theHindmarsh-Rose neuron with completely nearest-neighbor connections. In our numerical studies, a stable rotating spiralwave is developed and selected as the initial state, then the bifurcation parameters are changed to different values toobserve the transition from spiral wave to homogeneous state, breakup of spiral wave and weak change of spiral wave,respectively. A statistical factor of synchronization is defined with the mean field theory to analyze the transition fromspiral wave to other spatial states, and the snapshots of the membrane potentials of all neurons and time series of meanmembrane potentials of all neurons are also plotted to discuss the change of spiral wave. It is found that the sharpchanging points in the curve for factor of synchronization vs. bifurcation parameter indicate sudden transition fromspiral wave to other states. And the results are independent of the number of neurons we used.

Segmented Spiral Waves and Anti-phase Synchronization in a Model System with Two Identical Time-Delayed Coupled Layers

In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spiral waves, which are constituted by many thin trips, are found in each layer of two identical time-delayed coupled layers, and are different from the segmented spiral waves in a water-in-oil aerosol sodium bis（2-ethylhexyl） sulfosuccinate （AOT） microemulsion （ME） （BZ-AOT system）, which consists of many small segments. ＂Anti-phase spiral wave synchronization＂ can be realized between the first layer and the second one. For different excitable parameters, we also give the minimum values of the coupling strength to generate segmented spiral waves and the tip orbits of spiral waves in the whole bilayer.

Control of Spiral Waves and Spatiotemporal Chaos by Exciting Travel Wave Trains

Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.

Elimination of spiral waves and spatiotemporal chaos by the pulse with a specific spatiotemporal configuration

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time （to）. When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications.

The effect of cellular aging on the dynamics of spiral waves

Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg–Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves,the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly.

Formation and instability of spiral wave induced by Gaussian coloured noise

In this paper, we studied the effect of Gaussian coloured noise on the formation and instability of spiral waves described by one class of modified FitzHugh Nagumo equation. It was found that Gaussian coloured noise plays a constructive role in the formation, transition and instability of spiral wave. Too weak or too strong noise may act against the formation of spiral waves. At a certain noise level, spiral wave is maintained in a medium, in which spiral wave cannot be observed in the absence of the noise. It is difficult to make a stable spiral wave into unstable state by Gaussian coloured noise, unless the noise level is very high. The parameter regions of Gaussian coloured noise for spiral forming and spiral instability were given and discussed with numerical simulations.

Dynamics of Meandering Spiral Waves Driven by Two-Point Feedback

We numerically study the dynamics of meandering spiral waves in the excitable system subjected to a feedback signal coming from two measuring points located on a straight line together with the initial spiral core. The core location and size radius of the final attractors are computed, and they change with the position of the moving measuring point in a unique way. By the Fourier Spectral analysis, we find the frequency-locked behaviors different from the driving scheme of the external periodic force. It when the moving measuring point approaches closely is also found that the meandering spiral wave can be eliminated the boundary and its feedback gain is large enough. This offers an effective and convenient method for eliminating meandering spiral waves.

Theoretical Study on Drift of Ca^(2+)Spiral Waves Controlled by Electric Field

Based on the Tang-Othmer Ca^2＋ model, the drift behavior of intracellular Ca^2＋ spiral waves under the influence of weak electric field is investigated. Numerical results show that the dependence of drift velocity of the spiral tip on dc electric field is similar to experimental observations in BZ system. When an ac electric field is applied, interesting resonant-drift phenomenon is observed with ω=2ω0. All results can be explained analytically using a proximate method.

Dynamics of Spiral Wave Tip in Excitable Media with Gradient Parameter

Using a Barkley model as an example, we study spirM waves and spiral tips in a gradient excitable medium. The gradient distribution of parameters is introduced to depict the inhomogeneous medium. It is found that the parameter fluctuations play an important role in the morphology of spiral pattern and the movements of spiral tips. For varied gradient parameters, it is observed that there exist three kinds of spiral behaviors, stable rotation, rebound of spiral tip from the boundary, and spiral breakup.

Suppression of Spiral Wave in Modified Orengonator Model

In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Ф is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Ф changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh-Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the soiral turbulence.

Drift of Spiral Waves in Complex Ginzburg-Landau Equation

The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations.

Elimination of spiral waves and spatiotemporal chaos by the synchronization transmission technology of network signals

A method to eliminate spiral waves and spatiotemporal chaos by using the synchronization transmission technology of network signals is proposed in this paper. The character of the spiral waves and the spatiotemporal chaos in the Fitzhugh-Nagumo model is presented. The network error evolution equation with spatiotemporal variables and the corresponding eigenvalue equation are determined based on the stability theory, and the global synchronization condition is obtained. Simulations are made in a complex network with Fitzhugh-Nagumo models as the nodes to verify the effectiveness of the synchronization transmission principle of the network signal.