Noise-induced complex dynamics and synchronization in the map-based Chialvo neuron model
The aim in this article is an experimentally investigation of the neuron activity, actually a numerical study on how noise influences the dynamics of a neural network. As prototype, the quite simple map-based Chialvo neuron model described in the work of \textit{D. R. Chialvo} [Chaos Solitons Fractals 5, No. 3--4, 461--479 (1995; Zbl 0925.92020)], is considered. In the second section of the paper, one introduces the deterministic Chialvo model \[ x_{t+1}={x_t}^2\exp(y_t-x_t)+I \] \[ y_{t+1}=ay_t-bx_t+c \] where \(x\) stands for the activation variable, \(y\) for the recovery, \(I\) models the action of the ion current injected into the neuron and parameter \(a,b,c\) characterize recovery process. For different values of \(a,b,c\) and \(I\), the system behavior is discussed and diagrams are shown. In the third section one extends the investigation to a stochastic model obtained by adding to the first equation of the considered Chialvo model, a noise \(\epsilon\xi_t\). Experiments for different values of \(I\) and the noise intensity \(\epsilon\) are performed, results are plotted, discussed and interpreted. In the fourth section one analyzes the effects of the noise on a two-neurons network. The aim is to study the synchronization between the neurons due to noise effects. The complete model of the network is presented and for different model parameters the time series of both neurons are plotted. Further, in the fifth section, by varying model parameter and noise one obtains numerical evidence for the synchronization process. Conclusions and discussion are to be found in the sixth section.
scientific article; zbMATH DE number 7609364