Abstract
The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. Synchronization between a driving FOCVCNN and a response FOCVCNN, as well as the identification of unknown parameters are implemented. Based on fractional complex-valued inequalities and stability theory of fractional-order chaotic complex-valued systems, the paper designs suitable adaptive controllers and complex update laws. Moreover, it scientifically estimates the uncertainties and external disturbances to establish the stability of controlled systems. The computer simulation results verify the correctness of the proposed method. Not only a new method for analyzing FOCVCNNs with time-delay and unknown complex parameters is provided, but also a sensitive decrease of the computational and analytical complexity.
Highlights
Compared with real-valued neural networks, complex-valued neural networks have the advantages of simpler network structure, simpler training process, and stronger ability to handle complex signals
This is mainly due to the fact that the state vectors, connection weights, and activation functions in complex-valued neural networks are all represented by complex values
Inspired by the above discussion, this paper investigates the synchronization problem of FOCVCNNs with time-delay and unknown complex parameters
Summary
Compared with real-valued neural networks, complex-valued neural networks have the advantages of simpler network structure, simpler training process, and stronger ability to handle complex signals. Authors in [37] investigated the controller design problem for finite-time and fixed-time stabilization of fractional-order memristive complex-valued bidirectional associative memory (BAM) neural networks with uncertain parameters and time-varying delays, but the nonlinear complex-valued activation functions are split into two (real and imaginary) components. To the best of our knowledge, there are few studies on the synchronization of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delays and unknown parameters, especially without dividing the real and imaginary components into two real-valued systems. It is very important and useful to efficiently synchronize fractional-order complex-valued chaotic neural networks with time-delays and unknown parameters in practical applications. A new adaptive controller and update laws are designed to synchronize the driving and response systems This is the first study of synchronization of fractional-order complex-valued neural networks with time-delay and unknown complex parameters. (v) This paper proposes the novel perspective that chaos occurs in fractional-order complex-valued neural networks as long as the parameters are suitable, and two new FOCVCNNs are given to broaden the application of fractional-order complex-valued neural networks
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