Spatiotemporal chaos control with a target wave in the complex Ginzburg-Landau equation system

Abstract

An effective method for controlling spiral turbulence in spatially extended systems is realized by introducing a spatially localized inhomogeneity into a two-dimensional system described by the complex Ginzburg-Landau equation. Our numerical simulations show that with the introduction of the inhomogeneity, a target wave can be produced, which will sweep all spiral defects out of the boundary of the system. The effects exist in certain parameter regions where the spiral waves are absolutely unstable. A theoretical explanation is given to reveal the underlying mechanism.

Target patterns in two-dimensional heterogeneous oscillatory reaction–diffusion systems

“…The model investigated in this paper has also been used to study how target waves emitted by a pacemaker may suppress spatio-temporal turbulence observed in the two-dimensional medium [11].…”

“…Most basic features of such patterns already were described by the beginning of the 1980s [3][4][5][6], but since then target patterns have received less attention than, e.g., rotating spiral waves. Recently, renewed interest in target patterns and pacemakers has yielded considerable progress in the understanding of these patterns [7][8][9][10][11][12][13].…”

Heterogeneity selected target waves and their competition: Outgoing or ingoing?

“…The existence of the great majority of target waves in practice is attributed to a local heterogeneity (e.g., a dust particle, gas bubble, etc.) that plays the role of a pacemaker [2,[6][7][8][9][10][11][12][13][14][15][16], while self-organized target waves are also found both in several models [17][18][19] and in the experiments [20]. Theoretical studies on the heterogeneity sustained target patterns have also been provided [21,22], which makes us understand better the mechanism underlying the formation of target waves.…”

Numerical Studies Based on Higher-Order Accuracy Lattice Boltzmann Model for the Complex Ginzburg-Landau Equation

“…It has wide application in the fields of nonlinear wave, superconductivity, super fluidity, pattern formation, instabilities in non-equilibrium fluid dynamics, chemical system [63], even that in nonlinear optics [64,65], and spatiotemporal chaos [66] in different regime of parameters under appropriate initial conditions etc.…”

“…CGLE can be used to study not only the traveling wave solutions [65][66][67][68], but also the spiral wave and the scroll wave [69][70][71][72]. The spiral wave in 2D space and the scroll wave in 3D space are usually encountered in the systems driven away from equilibrium.…”