Emergence, Competition and Dynamical Stabilization of Dissipative Rotating Spiral Waves in an Excitable Medium: A Computational Model Based on Cellular Automata

We report some qualitatively new features of emergence, competition and dynamical stabilization of dissipative rotating spiral waves (RSWs) in the cellular-automaton model of laser-like excitable media proposed in arXiv:cond-mat/0410460v2 ; arXiv:cond-mat/0602345 . Part of the observed features are caused by unusual mechanism of excitation vorticity when the RSW's core get into the surface layer of an active medium. Instead of the well known scenario of RSW collapse, which takes place after collision of RSW's core with absorbing boundary, we observed complicated transformations of the core leading to regeneration (nonlinear "reflection" from the boundary) of the RSW or even to birth of several new RSWs in the surface layer. Computer experiments on bottlenecked evolution of such the RSW-ensembles (vortex matter) are reported and a possible explanation of real experiments on spin-lattice relaxation in dilute paramagnets is proposed on the basis of an analysis of the RSWs dynamics. Chimera states in RSW-ensembles are revealed and compared with analogous states in ensembles of nonlocally coupled oscillators. Generally, our computer experiments have shown that vortex matter states in laser-like excitable media have some important features of aggregate states of the usual matter.

Numerical Modeling of Coexistence, Competition and Collapse of Rotating Spiral Waves in Three-Level Excitable Media with Discrete Active Centers and Absorbing Boundaries

Spatio-temporal dynamics of excitable media with discrete three-level active centers (ACs) and absorbing boundaries is studied numerically by means of a deterministic three-level model (see S. D. Makovetskiy and D. N. Makovetskii, on-line preprint cond-mat/0410460 ), which is a generalization of Zykov- Mikhailov model (see Sov. Phys. -- Doklady, 1986, Vol.31, No.1, P.51) for the case of two-channel diffusion of excitations. In particular, we revealed some qualitatively new features of coexistence, competition and collapse of rotating spiral waves (RSWs) in three-level excitable media under conditions of strong influence of the second channel of diffusion. Part of these features are caused by unusual mechanism of RSWs evolution when RSW's cores get into the surface layer of an active medium (i.~e. the layer of ACs resided at the absorbing boundary). Instead of well known scenario of RSW collapse, which takes place after collision of RSW's core with absorbing boundary, we observed complicated transformations of the core leading to nonlinear ''reflection'' of the RSW from the boundary or even to birth of several new RSWs in the surface layer. To our knowledge, such nonlinear ''reflections'' of RSWs and resulting die hard vorticity in excitable media with absorbing boundaries were unknown earlier. ACM classes: F.1.1, I.6, J.2; PACS numbers: 05.65.+b, 07.05.Tp, 82.20.Wt

A Computational Study of Rotating Spiral Waves and Spatio-Temporal Transient Chaos in a Deterministic Three-Level Active System

Spatio-temporal dynamics of a deterministic three-level cellular automaton (TLCA) of Zykov-Mikhailov type (Sov. Phys. - Dokl., 1986, Vol.31, No.1, P.51) is studied numerically. Evolution of spatial structures is investigated both for the original Zykov-Mikhailov model (which is applicable to, for example, Belousov-Zhabotinskii chemical reactions) and for proposed by us TLCA, which is a generalization of Zykov-Mikhailov model for the case of two-channel diffusion. Such the TLCA is a minimal model for an excitable medium of microwave phonon laser, called phaser (D. N. Makovetskii, Tech. Phys., 2004, Vol.49, No.2, P.224; cond-mat/0402640). The most interesting observed forms of TLCA dynamics are as follows: (a) spatio-temporal transient chaos in form of highly bottlenecked collective evolution of excitations by rotating spiral waves (RSW) with variable topological charges; (b) competition of left-handed and right-handed RSW with unexpected features, including self-induced alteration of integral effective topological charge; (c) transient chimera states, i.e. coexistence of regular and chaotic domains in TLCA patterns; (d) branching of TLCA states with different symmetry which may lead to full restoring of symmetry of imperfect starting pattern. Phenomena (a) and (c) are directly related to phaser dynamics features observed earlier in real experiments at liquid helium temperatures on corundum crystals doped by iron-group ions. ACM: F.1.1, I.6, J.2; PACS:05.65.+b, 07.05.Tp, 82.20.Wt