Calculation of stability domains of discrete models of big size small world networks

The article is devoted to description of discrete models of small world networks with a large number of neurons with a certain parameter $p$ varying from $0$ to $1$. For $p = 0$ have model, regular neural networks, which is a ring network in which each neuron interacts with several neighbors on the ring. In the case $p = 1$ have a model with randomly distributed connections. When the values of $p$ not exceeding $0,1$ have the Watts–Strogatz small world network. Such a neural network can be models of different neural structures in living organisms, for example, the hipocampus of the mammalian brain. This paper examines the dynamics of change areas of stability of such neural networks when $0 \leqslant p\leqslant 0,1$. Numerical experiments show an increase in sustainability in the transition from a regular network to small world.