Extreme Multistability of a Fractional-Order Discrete-Time Neural Network

At present, the extreme multistability of fractional order neural networks are gaining much interest from researchers. In this paper, by utilizing the fractional I-Caputo operator, a simple fractional order discrete-time neural network with three neurons is introduced. The dynamic of this model are experimentally investigated via the maximum Lyapunov exponent, phase portraits, and bifurcation diagrams. Numerical simulation demonstrates that the new network has various types of coexisting attractors. Moreover, it is of note that the interesting phenomena of extreme multistability is discovered, i.e., the coexistence of symmetric multiple attractors.

Automated summary

In this paper, a simple fractional order discrete-time neural network with three neurons is introduced using the fractional I-Caputo operator. Experimentally investigated dynamics of this model show various types of coexisting attractors, as well as the interesting phenomena of extreme multistability, i.e. the coexistence of symmetric multiple attractors.