Synchronization Control Of Fractional-Order Complex-Valued Neural Networks

Over the past decades,artificial neural networks have been a highly sought-after area of study in the field of AI.Artificial neural networks are highly robust,can learn and self-adapt to unknown systems and can process large amounts of knowledge in parallel.Therefore,artificial neural networks have been successfully applied in various fields such as secure communication and pattern recognition.The study of the dynamical properties of neural networks provides the theoretical support for their powerful functions.Synchronization,as a typical characteristic of nonlinear system dynamics,has important theoretical research value as well as practical application value.Fractional-order neural networks have stronger memory capacity than integer-order neural networks and can describe the dynamical behavior of the system more accurately.Therefore,fractional-order neural networks are closer to realistic models,and it is of great research significance and application value to study synchronization control of fractional-order neural networks.Moreover,complex-valued signals exist widely in the real world,with more intricate dynamics and broader practical applications than those of real-valued systems,so it is very valuable and necessary to extend the study of neural networks to the complex domain.Additionally,the influence of uncertainty of some parameters in neural networks cannot be ignored.The introduction of fuzzy logic into neural networks can reduce the system’s requirement for accuracy and effectively handle complex fuzzy input information.Based on the above analysis,this paper investigates several synchronization problems of fractional-order complex-valued neural networks using different control methods from theoretical research and practical applications,and applies the theoretical research results to the field of secure communication.The primary task of the full paper is as follows:(1)The synchronization problem of complex-valued neural networks with time-varying time lags is investigated without separating the complex-valued systems.First,two new fractional-order differential inequality theorems with time lag are proposed,which provide new ideas for studying the adaptive synchronization of time-lagged fractional-order systems.Secondly,based on these two inequality theorems and the adaptive control strategy,the conditions for the system to achieve complete synchronization and proposed projection synchronization are obtained by using Lyapunov stability theory.The correctness of the results is verified by the final simulation example.(2)Combining fractional-order neural networks and fuzzy logic,the finite-time synchronization of fractional-order fuzzy system is explored in the complex domain.An effective and flexible negative feedback control strategy is designed.By utilizing the controller and the Lyapunov stability technique,we can ascertain the conditions for the system to attain finite-time full synchronization and finite-time projection synchronization and calculate the synchronization time,respectively.The research results related to fractional-order fuzzy neural networks are broadened in the complex domain.(3)Based on the above research,the wave signal encryption scheme based on fractionalorder complex-valued neural network adaptive synchronization and the image encryption scheme based on fractional-order fuzzy complex-valued neural network finite-time synchronization are proposed based on the basic principle of chaotic confidential communication.The previons theoretical study on synchronization of fractional-order complex-valued neural networks is applied to the field of secure communication.The implementation of theory to application is completed.