ELSEVIER Physica D 100 (1997) 330-342 PHYSICA Spatial disorder and pattern formation in lattices of coupled bistable elements V.I. Nekorkin a,,, V.A. Makarov a, V.B. Kazantsev a, M.G. Velarde b,l a Radiophysical Department, Nizhny Novgorod State University, 23 Gagarin av., 603600, Nizhny Novgorod, Russian Federation b Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, No. 1, Madrid 28 040, Spain Received 16 February 1996; revised 10 August 1996; accepted 26 August 1996 Communicated by A.V. Holden Abstract The spatio-temporal dynamics of discrete lattices of coupled bistable elements is considered. It is shown that both regular and chaotic spatial field distributions can be realized depending on parameter values and initial conditions. For illustration, we provide results for two lattice systems: the FitzHugh-Nagumo model and a network of coupled bistable oscillators. For the latter we also prove the existence of phase clusters, with phase locking of elements in each cluster. Keywords: Spatial disorder; Patterns; Bistable oscillators; Reaction-diffusion;Lattices 1. Introduction In recent years there has been a growing interest in the study of the collective behavior of active networks consisting of coupled nonlinear elements. On the one hand, such networks mimic spatially extended nonlinear systems paradigmatic for the evolution of nonequilibrium media. On the other hand, active networks have numerous applications [ 1-3]. In particular, systems consisting of a large number of bistable elements play a significant role. Bistability (i.e., coexistence of two attractors) is an outstanding property of nonlinear systems. It is clear that the bistability of elements can drastically influence the dynamics of a network and may result in nontrivial spatial effects. The spatio-temporal behavior of networks represented by coupled identical elements ordered in space is described by chain (one-dimensional networks) or lattice (multi-dimensional networks) dynamical systems. Refs. [4-9] deal with the discrete FitzHugh-Nagumo equation describing networks of diffusively coupled ex- citable cells. Conditions for the apparent "failure" of wave propagation connected with the multistability of the system and the conditions for propagation of wave fronts have been obtained. In [10] the stationary states of net- works consisting of weakly coupled bistable cells are studied. For systems of rather general type a method to estimate * Corresponding author. E-mail: nekorkin @rf.unn.runnet.rn. 1 E-mail: mvelarde@pluri.ucm.es. 0167o2789/97/$17.00 Copyright© 1997 Elsevier Science B.V. All rights reserved PH S01 67-2789(96)00202-3