Abstract
In the paper, a new adaptive model of a neuron based on the Hindmarsh–Rose third-order model of a single neuron is proposed. The learning algorithm for adaptive identification of the neuron parameters is proposed and analyzed both theoretically and by computer simulation. The proposed algorithm is based on the Lyapunov functions approach and reduced adaptive observer. It allows one to estimate parameters of the population of the neurons if they are synchronized. The rigorous stability conditions for synchronization and identification are presented.
Highlights
In [16], an approach based on adaptive observers was developed for partial identification HR model parameters
Andreev and Maksimenko [24] considered synchronization in a coupled neural network with inhibitory coupling. It was shown in [24] that in the case of a discrete neuron model, the periodic dynamics are manifested in the alternate excitation of various neural ensembles, whereas periodic modulation of the synchronization index of neural ensembles was observed in the continuous-time model
The following proposition concerning the convergence of the adaptive model to the true one holds
Summary
In [12], an approach to solving the problem of identifying topology and parameters in HR neural networks was proposed. For this purpose, the so-called generalized extremal optimization (GEO) was introduced, and a heuristic identification algorithm was employed. In [16], an approach based on adaptive observers was developed for partial identification HR model parameters. Malik and Mir [17] studied the synchronization of HR neurons, demonstrating that the coupled system shows several behaviors depending on the parameters of the HR model and coupling function. Andreev and Maksimenko [24] considered synchronization in a coupled neural network with inhibitory coupling It was shown in [24] that in the case of a discrete neuron model, the periodic dynamics are manifested in the alternate excitation of various neural ensembles, whereas periodic modulation of the synchronization index of neural ensembles was observed in the continuous-time model.
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