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

2004/10/19 by S. D. Makovetskiy, Makovetskiy, S. D., D. N. Makovetskii +1 · 5 citations
Computer Science · Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Computer and information sciences #FOS: Physical sciences #Neural and Evolutionary Computing (cs.NE) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Other Condensed Matter (cond-mat.other) #Quantum chaos and dynamical systems #cond-mat.other #cs.NE #nlin.CG

paper · pdf · doi:10.48550/arxiv.cond-mat/0410460

24 pages (LaTeX2e file) and 14 figures (separate PNG-files); Version 2 - minor changes and corrections, new references

openalex publication_date 2004/10/19 · arxiv created 2005/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• Emergence, Competition and Dynamical Stabilization of Dissipative Rotating Spiral Waves in an Excitable Medium: A Computational Model Based on Cellular Automata
• Microwave Power Spectra of Stimulated Phonon Emission and Spatio-Temporal Structures in an Optical-Wavelengths Acoustic Laser (Paramagnetic Phaser)
• Self-Organized Bottleneck and Coexistence of Incongruous States in a Microwave Phonon Laser (Phaser)
• Competition of Self-Organized Rotating Spiral Autowaves in a Nonequilibrium Dissipative System of Three-Level Phaser
• Dynamical Phenomena in an Optical-Wavelength Phonon Laser (Phaser): Nonlinear Resonances and Self-Organized Mode Alternation

Related

• Emergence, Competition and Dynamical Stabilization of Dissipative Rotating Spiral Waves in an Excitable Medium: A Computational Model Based on Cellular Automata
• Self-Organized Bottleneck and Coexistence of Incongruous States in a Microwave Phonon Laser (Phaser)
• Numerical Modeling of Coexistence, Competition and Collapse of Rotating Spiral Waves in Three-Level Excitable Media with Discrete Active Centers and Absorbing Boundaries
• Asymptotic Behavior of Excitable Cellular Automata
• Multi-state stochastic hotchpotch model gives rise to the observed mesoscopic behaviour in the non-stirred Belousov--Zhabotinsky reaction