Emergence of spiral wave induced by defects block

Dynamics of spiral waves driven by a rotating electric field

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.

Selection of Spiral Wave in the Coupled Network Under Gaussian Colored Noise

We present a method for mesoscopic, dynamic Monte Carlo simulations of pattern formation in excitable reaction–diffusion systems. Using a two-level parallelization approach, our simulations cover the whole range of the parameter space, from the noise-dominated low-particle number regime to the quasi-deterministic high-particle number limit. Three qualitatively different case studies are performed that stand exemplary for the wide variety of excitable systems. We present mesoscopic stochastic simulations of the Gray-Scott model, of a simplified model for intracellular Ca oscillations and, for the first time, of the Oregonator model. We achieve simulations with up to particles. The software and the model files are freely available and researchers can use the models to reproduce our results or adapt and refine them for further exploration.

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Stochastic simulations of pattern formation in excitable media.

Visual scan paths exhibit complex, stochastic dynamics. Even during visual fixation, the eye is in constant motion. Fixational drift and tremor are thought to reflect fluctuations in the persistent neural activity of neural integrators in the oculomotor brainstem, which integrate sequences of transient saccadic velocity signals into a short term memory of eye position. Despite intensive research and much progress, the precise mechanisms by which oculomotor posture is maintained remain elusive. Drift exhibits a stochastic statistical profile which has been modelled using random walk formalisms. Tremor is widely dismissed as noise. Here we focus on the dynamical profile of fixational tremor, and argue that tremor may be a signal which usefully reflects the workings of the oculomotor postural control. We identify signatures reminiscent of a certain flavour of transient neurodynamics; toric travelling waves which rotate around a central phase singularity. Spiral waves play an organisational role in dynamical systems at many scales throughout nature, though their potential functional role in brain activity remains a matter of educated speculation. Spiral waves have a repertoire of functionally interesting dynamical properties, including persistence, which suggest that they could in theory contribute to persistent neural activity in the oculomotor postural control system. Whilst speculative, the singularity hypothesis of oculomotor postural control implies testable predictions, and could provide the beginnings of an integrated dynamical framework for eye movements across scales.

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Capture of fixation by rotational flow; a deterministic hypothesis regarding scaling and stochasticity in fixational eye movements.

We investigate the jointly driven effects of external periodic forcing and Gaussian white noise on meandering spiral waves in excitable media with FitzHugh–Nagumo local dynamics. Interesting phenomena resulted from various forcing periods are found, for example, piece-wise line drift, intermittent straight-line drift and so on. We also observe new type of breakup of spiral wave between entrainment bands with 1:1 and 2:1. It is believed that the occurrence of the new type is relevant to the appearance of local bidirectional propagation window. There exist optimized noise intensities which can induce the broadest entrainments and Arnold tongues. Such a phenomenon is referred to as stochastic resonance. It is also observed that the noise makes significant effects on the spiral wave with straight-line drift. Via the tip Fourier spectrum, the varying of tip motion with external periods on the resonance band is interpreted.

Spiral waves in excitable media due to noise and periodic forcing

In this paper, a shell model for the energy cascade in three-dimensional turbulence at varying the viscosity is studied. When the viscosity parameter ν is large enough, the phase orbit of each shell in the system is a stable fixed point. As ν diminishes down to a critical value, the point becomes unstable and a stable periodic orbit appears via a supercritical Hopf bifurcation. For the quasiperiodic solution of the system, each shell has a own dynamic behavior. At ν = 6.88×10-5, the system initiates a complex scenario of bifurcations, where the phase orbits of un and un+3 begin to form a intersected section. Farther decreasing ν, we observe a transition from quasiperiodic solution to chaos through a sequence of Neimark–Sacker bifurcations. The behaviors can be vividly shown in the change of the average energy function E with ν. At last, the transition to chaos in the ν–δ parameter space is also obtained.

Transition to chaos in a shell model of turbulence with the change of the viscosity

Considering the intermittency of turbulence, the white noise as the stochastic driving term in time-varying stochastic turbulence model, which was supposed by Curtis R. Vogel [1], is replaced by a L\'{e}vy random process. Phase screens can be obtained by solving the stochastic partial differential equation (PDE), and the corresponding point spread function (PSF) is also offered. These results describe that intermittency leads to the more extent distribution of PSF and more bad imaging quality.

Lin Xu

Papers

Spiral waves in excitable media due to noise and periodic forcing

Transition to chaos in a shell model of turbulence with the change of the viscosity

Time-Varying Stochastic Turbulence Model Considering Intermittency