Synchronization Analysis Of Caputo-Type Fractional-Order Neural Networks With Mixed Delays

This paper mainly studies some synchronization behaviors of fractional-order neural networks,in which two different delays are considered at the same time.Caputo fractional derivative can be regarded as a formal generalization of integer derivative in the sense of Laplace transform,which is also convenient in engineering application.The definition of Caputo fractional derivative is adopted in this paper,and the mathematical model is established combined with neural networks.Using inequality technique,the sufficient criteria of finite-time synchronization,quasi-projection synchronization and quasi-uniform synchronization are derived.At the same time,the feasibility and rationality of the conclusions are verified by numerical simulation.Firstly,the fractional-order real-valued neural networks with discrete and distributed delays is constructed,and the finite time synchronization of the model is studied.Based on the theory of fractional calculus and inequality scaling,the sufficient conditions for the finite-time synchronization of the proposed model are derived.In order to verify the universality of the results,Matlab is used for numerical simulation.Then,the real-valued system is extended to the complex-valued,and the fractional-order neural networks is explored.In this model,both discrete delay and distributed delay are considered,and the quasi-projective synchronization problem is deeply analyzed.In order to reduce the difficulty of practical operation and the complexity of theoretical analysis,the complex-value systems is regarded as a whole.Two simple control strategies are selected,and an appropriate Lyapunov function is constructed.Using the idea of inequality expansion and contraction,the sufficient criteria for quasi-projection synchronization of the studied model are established.In addition,the error upper bound of quasi-projection synchronization is estimated.In order to illustrate the effectiveness of the results,Matlab is used for numerical verification.Finally,based on the fractional-order neural networks,two other delays,leakage delay and discrete delay,are considered,and the quasi-uniform synchronization problem is also discussed.Based on the properties of fractional calculus,combined with Laplace transform and inequality expansion and contraction.On order(0,2),the sufficient criteria for quasi-uniform synchronization of the model is derived.In order to prove the rationality of the results,mathematical software is used for numerical simulation.