ABSTRACT
In this paper the state and parameter estimation of an array of non-identical, locally connected chaotic biological neuronal models is considered. It is known that, under certain conditions, even a single biological neuron can exhibit chaotic behaviour. Chaos may be achieved by introducing the nonlinear effects of the chemical and electrical synapses. Alternately the chaotic behaviour of the single biological neuron is achieved by driving it with periodic excitations. The global behaviour of an array of biological neurons may then be investigated by considering a spatial distribution of identical neurons, where spatio-temporal chaos emerges, as well as in presence of spatial diversity, generated by a distribution law which could be stochastic or chaotic. In the latter case, it has been observed that the introduction of spatial disorder enhances the self-organization or synchronisation capability. In particular, in agreement with the results presented in Elson et al. [1], Pinto et al. [2] and Szücs et al. [3], the introduction of spatial diversity generated by such a distribution leads to an improvement in synchronization. While the phenomenon of synchronization in dynamical has been observed over a long time, two or more chaotic systems can be synchronized by linking them with mutual coupling or with a common signal or signals. Ideal synchronisation could be induced by mutually coupling a pair of identical chaotic systems when all trajectories converge to the same value and remain in step with each other during further evolution. Linking chaotic systems given by identical
differential-dynamic models but with different system parameters can lead to practical synchronization involving phase synchronization. Initially unexcited biological neural models, subsequently externally excited by periodic oscillators can synchronize both in chaotic and periodic regimes. Provided the amplitudes and frequencies of certain modes are within certain limits it has been observed that a number of independent neurons can exhibit periodic or chaotic behaviour and achieve a regime of complete synchronization including phase synchronization.
