Clusters of synchronization and bistability in lattices of chaotic neurons

– We investigated different regimes of synchronization in large lattices of chaotic spiking-bursting neurons. The lattices exhibit the following features: developed spatio-temporal disorder with no synchronization; spatial clusters of bursting synchronization; homogeneous bursting synchronization; and complete chaotic synchronization. We observed a bistable synchronization phenomenon in a wide region of the control parameter space. The bistability exists for homogeneous bursting synchronization with long-range correlation and spatial clusters of partial synchronization. The bistable regime appears in lattices with a size larger than the space-scale of these clusters. Introduction. – The analysis of the behavior of large assemblies of chaotic elements has been the subject of recent investigations, and is of interest both from the fundamental [1-5] and modeling points of view [6-9]. In particular, a network of chaotic elements is currently a very popular ingredient of information processing [7]. We report in this letter on the collective dynamics of chaotic neurons with local interactions. Recent work [3-6] indicates that such lattices often exhibit “non-trivial” cooperative behavior demonstrating a rich variety of phase transitions. Such behavior is “non-trivial” because the chaotic dynamics of these lattices with short-scale interaction must exhibit extensive chaos: the number of Lyapunov exponents increases with the size of the lattice (see, for example, [1, 2]). Actually, the cooperative behavior of chaotic lattices depends strongly on the strength of the local connection, variations of which reveal a rich diversity of synchronization. The model. – The lattice is made of non-identical Hindmarsh-Rose neurons [10] placed randomly inside the chaotic regime. Each element is electrically coupled to its nearest neighbors. c © EDP Sciences 720 EUROPHYSICS LETTERS 0 400 80