Existence uniqueness and stability analysis of solutions for the fractional fuzzy cellular neural networks with impulse and reaction diffusion
Xixi Xiong, Mei Xiong, Longwei Chen, Min Luo, Yimin Yu · Mathematical and Computer Modelling of Dynamical Systems · 2025
The existence, uniqueness and stability of the solution of a class of fractional-order delayed fuzzy cellular neural networks are discussed. Different from previous literature, the effects of reaction-diffusion, impulsive perturbations and time-varying delays are under consideration. The analysis can be applied to the qualitative theory of different classes of fractional-order neural network models in engineering, biology and medicine. First, the Lyapunov function method is used. A positive definite Lyapunov function is constructed, and parameters are computed to make its derivatives are negative definite, thus obtaining the global Mittag-Leffler stability criterion. Second, the compression mapping method is used to obtain the criterion of existence and uniqueness of the solution. The state update of a neural network can be viewed as a mapping, and if this mapping is compressed, there is a unique solution. Finally, two numerical examples are given to show the effectiveness and characteristics of the obtained theoretical results.