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Synchronization is known to play a vital role within many highly connected neural systems such as the olfactory systems of fish and insects. In this paper we show how one can robustly and effectively perform practical computations using small perturbations to a very simple globally coupled network of coupled oscillators. Computations are performed by exploiting the spatio-temporal dynamics of a robust attracting heteroclinic network (also referred to as `winnerless competition dynamics). We use different cluster synchronization states to encode memory states and use this to design a simple multi-base counter. The simulations indicate that this gives a robust computational system exploiting the natural dynamics of the system.
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle
Accumulating evidences show that the cerebral cortex is operating near a critical state featured by power-law size distribution of neural avalanche activities, yet evidence of this critical state in artificial neural networks mimicking the cerebral c
Substantial evidence indicates that the brain uses principles of non-linear dynamics in neural processes, providing inspiration for computing with nanoelectronic devices. However, training neural networks composed of dynamical nanodevices requires fi
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean fields. We der
In this paper, an explanation of the Newton-Peiseux algorithm is given. This explanation is supplemented with well-worked and explained examples of how to use the algorithm to find fractional power series expansions for all branches of a polynomial at the origin.