Second Universal Limit of Wave Segment Propagation in Excitable Media

Abstract

A free-boundary approach is applied to derive universal relationships between the excitability and the velocity and the shape of stabilized wave segments in a broad class of excitable media. In the earlier discovered low excitability limit wave segments approach critical fingers. We demonstrate the existence of a second universal limit (a motionless circular shaped spot) in highly excitable media. Analytically obtained asymptotic relationships and interpolation formula connecting both excitability limits are in good quantitative agreement with results from numerical simulations.

Polymorphic and regular localized activity structures in a two-dimensional two-component reaction–diffusion lattice with complex threshold excitation

“…That is, it has curvature which strongly depends on spatial coordinates. Note that regular structures obtained in two-component reaction-diffusion systems with different stabilizing actions [10,11,[28][29][30] have a similar asymmetric crescent-like shape. On the other hand, regular structures obtained in multi-component reaction-diffusion systems [24][25][26] are not asymmetric.…”

“…Due to the existence of such thresholds the unit in this case can display transient ''rotational'' oscillatory activity. Note that the presence of such nontrivial local dynamics completely distinguishes the system (1) from other twoa b component reaction-diffusion systems (see, for example, Zykov et al [28,29], Kobayashi et al [49]). We established that the presence of complex threshold excitability plays a crucial role in the formation of localized structures in the system (1).…”

“…There are several ways to achieve this. One of them is to apply a dynamical feedback to suppress the growth process [10,11,[27][28][29]. Other possibilities are to introduce a grid-like inhomogeneity [30] or a strong diffusion anisotropy setting, for example, significantly different diffusion coefficients along different spatial coordinates [31].…”

Algebraic segmentation of short nonstationary time series based on evolutionary prediction algorithms

“…In general, a proper segmentation of a time series provides a useful portrait of the local properties for investigating and modeling nonstationary systems [1]. Such segmentation serves as a valuable tool in different areas including physics [2][3][4], biology [5][6][7], image and signal processing [8,9] and other disciplines. A number of different segmentation techniques have been introduced and successfully exploited in various computational set-ups.…”

Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh–Nagumo model

“…A high-voltage electric shock is applied to a patient's chest to eliminate the irregular activation and to restore the regular rhythm. 5,6 Sakurai et al experimentally proved that the modified feedback control can track the trajectory of propagating waves. 2,3 In addition, the nonlinear phenomena in the Belousov-Zhabotinsky (BZ) reaction have attracted increasing interest.…”