In Neural networks : the official journal of the International Neural Network Society
This paper presents theoretical results on multiple asymptotical ω-periodicity of a state-dependent switching fractional-order neural network with time delays and sigmoidal activation functions. Firstly, by combining the geometrical properties of activation functions with the range of switching threshold, a partition of state space is given. Then, the conditions guaranteeing that the solutions can approach each other infinitely in each positive invariant set are derived. Furthermore, the S-asymptotical ω-periodicity and the convergence of solutions in positive invariant sets are discussed. It is worth noting that the number of attractors increases to 3n from 2n in a neural network without switching. Finally, three numerical examples are given to substantiate the theoretical results.
Ci Jingxuan, Guo Zhenyuan, Long Han, Wen Shiping, Huang Tingwen
2022-Oct-13
Delay, Fractional-order neural network, Multiple asymptotical ω-periodicity, State-dependent switching
