Global Control of Spiral Wave Dynamics in an Excitable Domain of Circular and Elliptical Shape

Abstract

Experiments performed in a thin layer of the Belousov-Zhabotinsky solution subjected to a global feedback demonstrate the existence of the resonance attractor for meandering spiral waves within a domain of circular shape. In an elliptical domain, the resonance attractor can be destroyed due to a saddle-node bifurcation induced by a variation of the domain eccentricity. This conclusion explains the experimentally observed anchoring of spiral waves at certain points of an elliptical domain and is in good quantitative agreement with numerical data obtained for the Oregonator model.

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

“…57 In the absence of the polymer gel (i.e., in the BZ solution), this two-variable, photosensitive Oregonator model has been used to successfully explain the observed experimental phenomena in a number of studies. [58][59][60][61] Within this model, F specifically accounts for the additional production of bromide ions that are due to illumination by light of a particular wavelength and F is assumed to be proportional to the light intensity. 57 The above approach allows us to reproduce the experimentally observed suppression of oscillations within BZ gels by visible light.…”

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

“…The feedback signals are obtained from wave activity measured at one or several detector points, along detector lines, or in a spatially extended control domain including global feedback control [8,9,20]. Varying the excitability of the light-sensitive BZ medium by changing the globally applied light intensity forces a spiral wave tip to describe a wide range of hypocycloidal and epicycloidal trajectories [21,22].…”

“…Several control strategies have been developed for purposeful manipulation of wave dynamics as the application of closed-loop or feedback-mediated control loops with and without delays [8][9][10][11] and open-loop control that includes external spatio-temporal forcing [10,[12][13][14], optimal control [15][16][17], and control by imposed geometric constraints and heterogeneities on the medium [18,19]. While feedback-mediated control relies on continuously monitoring of the system's state, open-loop control is based on a detailed knowledge of the system's dynamics and its parameters.…”

Asymmetric Target Patterns in One-Dimensional Oscillatory Media with Genuine Nonlocal Coupling

“…So far, the overwhelming part of studies focused on the two limiting cases of spatial coupling, namely, local or nearest neighbor coupling, and global all-to-all coupling with infinite coupling range. Lately, also the dynamics of systems in which both local and global coupling coexist has been investigated (see, e.g., [1][2][3][4][5][6]). …”