Multistability and global attractivity for fractional-order spiking neural networks

Fractional-Order Spiking Neural Network (FOSNN) has the characteristic of infinite memory and neural impulses, which can more accurately describe neural network systems and demonstrate higher precision data processing capabilities in artificial intelligence. The neural spiking leads to multiple equilibrium points coexisting in the networks system. Multistability analysis mainly studies the problem of the multiple equilibrium points, which helps to improve the robustness and reliability of the networks. However, fractional calculus and neural spiking increase the theoretical difficulty of multistability and attractivity analysis in neural networks, which is the main motivation to study and discuss. Firstly, for a Hopfield type of FOSNN with pulse activation functions, the solution existence is proved according to Filippov solutions. Secondly, the state space is divided and the sufficient conditions for multistability are proposed and proved by using fixed point theorem, Laplace transform, Mittag-Leffler function monotonicity analysis, etc. Furthermore, the boundedness and global attractivity of FOSNN are discussed based on fractional-order Lyapunov method. Finally, using the fractional-order prediction correction algorithm, some numerical examples are conducted in order to verify the correctness for all proposed results.