Instabilities of the resonance attractor for spiral waves in an excitable medium

Abstract Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

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SPATIOTEMPORAL IRREGULARITY IN A TWO-DIMENSIONAL MODEL OF CARDIAC TISSUE

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127491000142 ◽

1991 ◽

Vol 01 (01) ◽

pp. 219-225 ◽

Cited By ~ 57

Author(s):

A. V. PANFILOV ◽

A. V. HOLDEN

Keyword(s):

Cardiac Tissue ◽

Numerical Solutions ◽

Spiral Waves ◽

Excitable Medium ◽

Two Dimensional ◽

Dimensional Model ◽

Two Dimensional Model ◽

Solutions Of Equations

Meandering spiral waves are well-known solutions of equations that represent a two-dimensional excitable medium. Numerical solutions of a model for a sheet of cardiac tissue show transient meandering vortices that break down spontaneously into spatiotemporal irregularity.

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Spiral waves on circular and spherical domains of excitable medium

Physica D Nonlinear Phenomena ◽

10.1016/0167-2789(96)00145-5 ◽

1996 ◽

Vol 97 (1-3) ◽

pp. 322-332 ◽

Cited By ~ 36

Author(s):

V.S. Zykov ◽

S.C. Müller

Keyword(s):

Spiral Waves ◽

Excitable Medium ◽

Spherical Domains

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Coexistence of multiple spiral waves with independent frequencies in a heterogeneous excitable medium

Physical Review E ◽

10.1103/physreve.63.031905 ◽

2001 ◽

Vol 63 (3) ◽

Cited By ~ 35

Author(s):

Fagen Xie ◽

Zhilin Qu ◽

James N. Weiss ◽

Alan Garfinkel

Keyword(s):

Spiral Waves ◽

Excitable Medium

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EXCITABLE SPIRAL WAVES IN NEMATIC LIQUID CRYSTALS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127494000873 ◽

1994 ◽

Vol 04 (05) ◽

pp. 1173-1182 ◽

Cited By ~ 12

Author(s):

P. COULLET ◽

F. PLAZA

Keyword(s):

Liquid Crystals ◽

Electric Field ◽

Nematic Liquid Crystals ◽

Spiral Wave ◽

Spiral Waves ◽

Excitable Medium ◽

Ginzburg Landau ◽

Landau Model ◽

Excitable System ◽

Mechanical Analog

A mechanical analog of the chemical and biological excitable medium is proposed. In nematic liquid crystals, the Freedericksz transition induced by a rotating tilted electric field provides a simple example of such a mechanical excitable system. We study this transition, derive a Ginzburg-Landau model for it, and show that the excitable spiral wave can be produced from a retractable finger-like soliton in this context.

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