We describe a two-dimensional CNN array of resistively coupled Chua's circuits which can be designed to implement some elementary aspects of spatial recognition, namely, recognizing open curves from closed ones and locating the shortest path between two locations. In the latter, two situations are analyzed: flat and wrinkled surfaces. The two-dimensional CNN array of Chua's circuits is shown, for the first time, to be capable of finding the shortest path between two points on a wrinkled labyrinth. The performance of this parallel processing approach was examined using computer simulations although this method can be implemented in real time via VLSI technology.

Sprial breakup in the Belousov-Zhabotinsky reaction has been observed under the influence of an externally applied alternating electric current. The dynamic mechanism of this breakup is explained in the framework of this reaction. The dependence of the critical electric current amplitude on the period of the wave and on the excitability of the medium is analyzed. Spiral breakup is shown to provide a limit of validity of electric-field-induced drift of vortices in excitable media. Experimental results are complemented with numerical simulations provided by two- and three-variable Oregonator models.

Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics. PACS numbers: 82.40.Bj, 05.45.Jn, 47.54. + r Spirals are generic structures in extended nonequilibrium systems. They are characteristic of many reactiondiffusion systems [1], the most paradigmatic experimental example being the Belousov-Zhabotinsky (BZ) reaction [2], and they have been observed in systems as complex as the heart muscle associated to cardiac fibrillation [3,4]. Spiral patterns appear also as elementary solutions of the complex Ginzburg-Landau (CGL) equation [5].Beyond the standard description of spiral waves, their response to spatial and/or temporal forcing has been largely analyzed. Temporal resonance [6], drift of vortices due to parameter gradients [7,8] or external fields [9], and anchoring on localized defects [10] are among the most studied effects.On the other hand, the influence of random heterogeneities on extended excitable systems has recently attracted much attention. Noise as an initiator of new spatial structures [11][12][13], or sustaining wave propagation in subexcitable media [14][15][16], is a subject of much theoretical and experimental interest. Complementarily, the role of superimposed disorder on preexisting spatiotemporal patterns has been examined, in relation to propagating pulses [17], to the dynamics of CGL spirals [18] and 3D structures [19].In this paper, we study the effect of a spatiotemporal structured noise on the motion of a spiral wave for the photosensitive BZ reaction. In the absence of randomness, the spiral tip rotates quasirigidly around its core, with no net translational mobility. When the noise is switched on, Brownian diffusion of the spiral is observed, characterized by a nonmonotonous dependence on the parameters of the noise. These observations are confirmed numerically using a two-variable Oregonator model. The analysis is completed by proposing a simple theoretical model based on a kinematic approach [20], capturing the basic features observed in experiments.Experiments were carried out in a Petri dish of 9 cm diameter. The catalyst, ruthenium bipyridil, is immobilized in a thin, 1 mm thick, film of silica gel, prepared as in [21].A solution of catalyst-free BZ reaction (initial concentrations 0.18M KBr, 0.33M malonic acid, 0.39M NaBrO 3 , and 0.50M H 2 SO 4 ) was poured onto the gel. The temperature was kept constant at 25 6 1 ± C. Spatiotemporal noise is introduced by projecting on to the Petri dish the desired patterned illumination, controlling the excitability of the system, by means of a video projector (SONY CPJ-D500). Experiments were capt...

We report on the discovery of a transition in rings of coupled electronic circuits in the chaotic regime to a collective periodic state characterized by a time scale that is between two and three orders faster than that corresponding to an isolated circuit. This transition arises from a linear instability in the uniform synchronized state of the ring through a symmetric Hopf bifurcation. The same type of transition is also observed for other coupled chaotic systems, e.g., a ring of Lorenz attractors.

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