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...
A method is presented for probing chemical reaction mechanisms experimentally with perturbations and measurements of the response. Time series analysis and the methods of linear control theory are used to determine the Jacobian matrix of a reaction at a stable stationary state subjected to random perturbations. The method is demonstrated with time series of a model system, and its performance in the presence of noise is examined.
In a tissue of oscillatory cells the active intracellular medium is surrounded by a membrane and the cells are separated by inactive extracellular medium. The synchronization properties of a system of such coupled oscillatory cells have been emulated using the light-sensitive Belousov-Zhabotinsky reaction. Experimental results for four coupled cells are confirmed by numerical simulations. We have furthermore demonstrated the existence of antispirals and antipacemaker waves with inward propagating waves in larger cell assemblies of this type. Such dynamical structures are extremely rare in homogeneous chemical systems where the generic behavior is normal spirals and target patterns with outward-moving waves.
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