Resonance drifts of spiral waves on media of periodic excitability

Abstract

Spiral waves subjected to an external periodic force exhibit very rich spatiotemporal dynamics including resonance attractors. In previous research, the modulation was mainly described as additional induced flow in the system, and a theory has been developed based on reducing the spiral wave dynamics to a low-dimensional map. In this paper, another perspective for study of the resonance attractors is suggested. The periodic modulation of excitability is directly described by the time dependence of the parameters. This approach gives us nice results that are well consistent with the experiments. Additionally, when we force the spiral with a frequency larger than its intrinsic frequency, another branch of spiral meandering with qualitatively different properties is observed. Full resonances are also clearly indicated. Furthermore, a kinetic model for spiral movement suggested in our previous paper is applied to this case. The theoretical results are in good quantitative agreement with numerical simulations. The model could be widely used in different excitable systems.

Asymptotic dynamics of reflecting spiral waves

“…By tracking either the local rotation center, or the closely related wave tip, one may observe interesting trajectories as drifting spirals move through a medium. * J.Langham@warwick.ac.uk † ivb@liverpool.ac.uk ‡ D.Barkley@warwick.ac.uk A noteworthy case is resonant drift [31][32][33][34][35][36][37][38][39][40] in which spatially uniform periodic driving is applied in resonance with the spiral rotation frequency. In this case the spiral core travels in a straight line with constant velocity.…”

“…However, a more detailed theoretical treatment is required to fully understand the mechanism behind spiral reflection. While separate theoretical accounts of both resonant drift [4,34,40,42,43] and spatial medium inhomogeneities [4,[44][45][46][47] (which may act as boundaries to drift) already exist, it is the combination and interaction of these two phenomena which we must consider here. A good candidate for an updated approach is to use the theory of response functions [1,2,4,42,43,46,48] which has developed and matured in the years since the Biktashev-Holden study.…”

Chaotic tip trajectories of a single spiral wave in the presence of heterogeneities

“…The waves can react to small perturbations as particle-like objects and asymptotic theories have been developed to describe their interactions with periodic perturbations and localized inhomogeneties [43,44]. Furthermore, previous studies have described the dynamics of spiral tips in terms of ordinary differential equations near bifurcation points [45,46] and have developed simple equations for circular tip trajectories in the presence of periodic modulations [47].…”

Pulsed low-energy stimulation initiates electric turbulence in cardiac tissue

“…In complex excitable systems, such as cardiac tissue, the dynamics of nonlinear spiral waves is determined primarily by the excitability of the medium. Hence, the modulation of excitability by, for example, varying its amplitude, frequency, degree of synchronization, and spatial scale, phenomena such as drift [11,12], deformation [13], block [13], meander [12,14], breakup [13,15], and suppression of spiral waves [16] can be observed. Of these phenomena, breakup essentially results in electric turbulence in the heart and is mediated by the formation of wavebreaks close to or away from the core of intact spirals.…”