Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

In recent years, exponential Euler difference methods have been widely used to discuss the neural network models depicted by integer order differential equations. However, it is rare to study fractional-order neural network models using such methods. Stimulated by this point, this paper firstly establishes Mittag-Leffler Euler difference for fractional-order fuzzy bidirectional associative memory neural networks, which includes exponential Euler difference. Secondly, global exponential stability and synchronization of the derived difference model are investigated. Compared with the classical fractional-order Euler difference method, the fuzzy Mittag-Leffler discrete-time bidirectional associative memory neural networks can better describe and maintain the dynamic properties of the corresponding continuous-time models. More importantly, it opens up a new way to study discrete-time fractional-order systems and builds a set of theory and methods to study Mittag-Leffler discrete neural networks.