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In this paper, we investigate the possibility to control the spiral waves and spatiotemporal chaos in an excitable media by subthreshold ordered waves, which is by definition in this paper the spatially ordered periodical subthreshold fluctuations of system variables. It is found that both the spiral wave and the spatiotemporal chaos could be driven out of the control domain by perturbation of periodical subthreshold ordered waves. The effective control time declines as the amplitude of subthreshold ordered waves are increased, or their frequencies are decreased. Furthermore, we show that the effectiveness of this method is also dependent on the spatial arrangement of the subthreshold ordered waves. We discuss the possible applications of this method, especially in the control of heart fibrillation.

A unidirectional coupling method to successfully suppress spiral waves in excitable media is proposed. It is shown that this control method has high control efficiency and is robust. It adapts to control of spiral waves for catalytic CO oxidation on platinum as well as for the FHN model. The power law n ~ c^-k of control time steps n versus the coupling strength c for different models has been obtained.

The selection and breakup of spiral wave in a coupled network is investigated by imposing Gaussian colored noise on the network, respectively. The dynamics of each node of the network is described by a simplified Chua circuit, and nodes are uniformly placed in a two-dimensional array with nearest-neighbor connection type. The transition of spiral wave is detected by changing the coupling intensity, intensity and correlation time τ in the noise. A statistical variable is used to discern the parameter region for breakup of spiral wave and robustness to external noise. Spiral waves emerge in the network when the network with structure of complex-periodic and chaotic properties. It is found that asymmetric coupling can induce deformation of spiral wave, stronger intensity or smaller correlation time in noise does cause breakup of the spiral wave.

In this paper, we propose the stochastic and unidirectional cross-coupled control method between two-layer excitable media to suppress the spiral waves and spatiotemporal chaos. Four types of the drive-response system in such two-layer excitable media are studied. By performing many simulations, results illustrate the spiral waves and spatiotemporal chaos can be controlled to the desired target states like the target waves and traveling waves. Patterns obtained are obviously different from those of the one-to-one coupling model. Based on the method proposed by Henry, we have carefully studied the generalized synchronization between the drive and response system with the stochastic and cross-connecting points via amplitude analysis and computing Poisson coefficient. Moreover, there also exists the frequency locking phenomenon.

In this paper, a modified Hindmarsh–Rose neuron model is presented, which has a fractional-order threshold magnetic flux. The dynamics of the model is investigated by bifurcation diagrams and Lyapunov exponents in two cases of presence and absence of the external electromagnetic induction. Then the emergence of the spiral waves in the network of the proposed model is studied. To find the effects of different factors on the formation and destruction of spiral waves, the external current, the coupling strength and the external stimuli amplitude are varied. It is observed that all of these parameters have significant impacts on the spiral waves. Furthermore, the external electromagnetic induction influences the existence of spiral waves in specific external current values.

We study wave propagation in a recently developed model, which reproduces geometry and fiber orientation in the right and left ventricles of the human heart. The cardiac tissue is represented using the previously developed γ-ionic model for human ventricular tissue using a spatial resolution of 0.5 mm. We simulate three-dimensional reentrant behavior resulting from a single vortex located in the free wall of the right, left ventricles and in the interventricular septum. We found that single reentrant scroll waves can generate V-shaped collision areas and in some cases, epicardial breakthrough patterns. The simulated ECGs of single spiral waves show similarities with monomorphic and polymorphic ventricular tachycardia, depending on the location of the reentrant sources. We model complex activation patterns resembling ventricular fibrillation by simulating the effects of an ATP-sensitive potassium channel opener and find that VF is, in that case, organized by a small number of vortices.

We investigate small two-dimensional arrays of locally coupled phase oscillators which are shown to exhibit a surprising variety of stable structures which include: single spiral waves, spiral pairs and spirals with secondary periodic core motion. This periodic core motion is not the core meander familiar to many models of active media, but is in fact induced by the boundary of the small domain. Such boundary motion was investigated by Sepulchre and Babloyantz [1993] for the complex Ginzburg–Landau equation and for the Brusselator model in a relaxation oscillation parameter regime. The current model confirms the findings in [Sepulchre & Babloyantz, 1993] and sheds new light on the origin of such motion. The model also exhibits other patterns, as well as a chaotic regime. We discuss the transition between patterns as the form of the coupling is changed as well as implications for pattern formation in general oscillatory media.

We investigate a spontaneous formation of stable multiarmed spirals in two-dimensional excitable media, an effect observed in various biological and chemical systems. A previous study based on FitzHugh–Nagumo-type Pushchino model reported a robust effect of stable two- and three-armed spiral formation from nearby vortices, when the spirals rotate around unexcited cores, i.e. when excitability of the medium is low. In this study, we used a powerful parallel computer cluster to perform an extensive parameter search in two other widely used FitzHugh–Nagumo-type models, as well as in the two-component Oregonator model. We observed formation of stable n-armed spirals, with 2 ≤ n ≤ 10, whenever the excitability of the medium was sufficiently low. Thus, we conclude that the formation and persistence of stable multiarmed spirals (MAS) is not an artifact of one particular model, but, rather, it is an amazing higher-level self-organization property of a generic weakly excitable medium. We also establish quantitatively that such multiarmed spirals serve as high-frequency wave sources — a finding that has a direct relevance to cardiac defibrillation research.

In this paper, we report on pattern formation occurring on the ACE16k CNN chip. The CNN chip can be programmed with a cloning template in order to generate spiral waves and autowaves. The waves diffract from internal sources which cannot be relocated on the network. However, by using initial and/or input images, sources (external sources) can be located at any place on the network. Furthermore a competition between autowaves generated by external and internal sources is observed. Propagation of autowaves on the inhomogeneous CNN array, formed by the fixed-state map, is presented.

Dynamics of spiral waves in perturbed, e.g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spirals Response Functions, which are eigenfunctions of the adjoint linearized problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh–Nagumo model, and show that they are effectively localized in the vicinity of the spiral core.

In this paper, the stochastic driving and coupling method to effectively suppress the turbulence and spiral waves is proposed. It is confirmed that the drive system ensures the response achieves complete synchronization via the computation of the Pearson's coefficient γ. The minimum time units of achieving complete synchronization N versus the coupling proportion P takes on the power-law N ~ P^-k.

Spatiotemporal dynamics of spiral tip and the evolution of spiral wave induced by external periodic modulation has been investigated in a generic excitable model. Tip dynamics of spiral wave depending on the frequency and strength of the external modulation is revealed by the meandering size variable R_x of the tip trajectory. Different effects of frequency and strength on spiral dynamics are observed and the corresponding mechanisms are explained. Finally, we can eliminate spiral wave out of the boundary successfully by suitably choosing the frequency and the strength of the external periodic modulation.

One-dimensional (1D) map-based neuron models are of significant interest according to their simplicity of simulation and ability to mimic real neurons’ complex behaviors. A fractional-order 1D neuron map is proposed in this paper. Dynamical characteristics of the model are analyzed by obtaining bifurcation diagrams and the Lyapunov exponents’ diagram. Furthermore, emerging the spiral wave as one of the most important collective behaviors is studied in a 2D lattice consisting of this new FO neuron model. The outcome of changing stimuli, coupling strength, and fractional-order parameter as the effective parameters is examined in this network. Moreover, an efficient way of suppressing the spiral wave has been investigated using impulse triggering.