Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 34, Issue 9, Pages 5476-5496Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2021.3129829
Keywords
Artificial neural networks; Synchronization; Mathematics; Delays; Stability criteria; Quaternions; Fractional calculus; Complex field; dynamical networks; fractional-order neural networks (FONNs); octonion field; quaternion field; stability; synchronization
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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.
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.
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