A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real (R), complex (C), quaternion (Q), and octonion (O) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

Automated summary

This study provides an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time. It covers various neural network models and their applications in different mathematical fields. Theoretical findings from multidimensional FONNs with different types of delays are thoroughly evaluated, and stability and synchronization requirements for fractional-order NNs without delays are mentioned.