Spatial Symmetry Breaking in the Belousov-Zhabotinsky Reaction with Light-Induced Remote Communication

Abstract

Domains containing spiral waves form on a stationary background in a photosensitive BelousovZhabotinsky reaction with light-induced alternating nonlocal feedback. Complex behavior of colliding and splitting wave fragments is found with feedback radii comparable to the spiral wavelength. A linear stability analysis of the uniform stationary states in an Oregonator model reveals a spatial symmetry breaking instability. Numerical simulations show behavior in agreement with that found experimentally and also predict a variety of other new patterns. DOI: 10.1103/PhysRevLett.87.088303 PACS numbers: 82.40.Ck, 05.65. +b, 47.54. +r, 82.30.Vy Physicochemical systems with coupled processes on different length scales often exhibit stationary spatially periodic structures arising from symmetry breaking instabilities [1][2][3]. In nonequilibrium systems, such structures occur in activator-inhibitor systems with short-range activation and long-range inhibition [1], while in equilibrium systems they arise from the competition of short-range attractive interactions and long-range repulsion [2]. Recent investigations also revealed spatial symmetry breaking arising from the interplay between short-range attractive interactions and a long-range reaction-diffusion process [3]. In this Letter, we report on novel spatiotemporal patterns in the photosensitive Belousov-Zhabotinsky (BZ) reaction [4] arising from a nonlocal feedback that imposes short-range activation and long-range inhibition.The photosensitive BZ reaction has proven to be an ideal model system for studies of perturbed excitable media. The medium excitability can be precisely controlled by exposure to 460 nm light, enabling the application of a wide variety of external perturbations. Entrainment of spiral wave meandering [5] and the formation of labyrinthine patterns [6] have been found with periodic forcing. Resonance attractors [7] and oscillatory cluster patterns [8] were recently reported in photosensitive BZ systems with different types of global feedback.We study the photosensitive BZ reaction with nonlocal coupling over a wide range of length scales, from much larger than the characteristic reaction-diffusion length scale to length scales that are comparable. The kernel of the feedback alternates from positive (activatory) for short distances to negative (inhibitory) for larger distances. We show below that such a feedback gives rise to a "Turinglike" instability, and, as a result, patterns with more than one characteristic length scale are formed.Experiments were carried out with the catalyst of the light-sensitive BZ reaction, Ru͑bpy͒ 21 3 , immobilized in a thin slab of silica gel. The gel was continuously fed with a fresh, catalyst-free BZ solution in a reactor thermostated at 23.0 ± C to maintain constant, nonequilibrium conditions [9]. The silica gel medium was prepared by acidifying a solution of 10% (w͞w) Na 2 SiO 3 and 2.0 mM Ru͑bpy͒ 21 3 with H 2 SO 4 and by casting a uniform 0.3 3 20.0 3 25.6 mm 3 layer onto a microscope slide. Prior to each experim...

Diffusive Instabilities and Chemical Reactions

“…Symmetry breaking takes place through the strong resonant forcing of spatially distributed oscillators as was theoretically proposed by Emilsson [1992a, 1992b] and finally experimentally observed and studied [Petrov et al, 1997;Lin et al, 2000]. Nonlocal feedbacks imposing long-range inhibition may readily give rise to pattern formation [Hildebrand et al, 2001;Mikhaïlov, 1994;Middya et al, 1993] when competing with some short-range activation process. Systematic studies of the spatial unfolding of elementary bifurcations have recently been set out by Coullet et al [2000].…”

Existence of pulses in excitable media with nonlocal coupling

“…Chemical reactions [1,18], calcium waves [33], and neural field models [5,6] are among the examples that motivate our present study. A prototypical model of excitable kinetics are the FitzHugh-Nagumo kinetics, derived first as a simplification of the Hodgkin-Huxley model for the propagation of electric signals through nerve fibers [19],…”

Mechanism and Phenomenology of an Oscillating Chemical Reaction

“…The photosensitive ruthenium-catalysed BZ reaction provides the ideal method for investigating global coupling in a spatially oscillating system. Vanag et al have demonstrated how global coupling in conjunction with local coupling can lead to the formation of stationary patterns, and "clustering" in which certain domains of the system display synchronous activity [355][356]. Showalter and coworkers were able to enhance the propagation of chemical waves in a subexcitable medium through the application of noise in the light intensity of a projected image [301].…”