Synchronization Of Coupled Duffing-type Oscillator Dynamical Networks

In the research of dynamic behavior,the synchronization research of inertial neural network has shown great potential in the fields of secure communication,image encryption and information science,so synchronization research should not be underestimated.According to the practical problems and applications,scholars have applied various methods to obtain multiple synchronization results,including Lyapunov functions,finite synchronization theory,matrix measure theory,integral inequality method.Based on the previous researches on synchronization,we are concerned with finite-time synchronization problems of delayed inertial neural networks via novel methods,by constructing integral inequality group and by means of using figure approach,constant variable method,and inequality skills.We discuss the finite-time synchronization for delayed inertial neural networks.The original system is transformed into two differential equations and one error differential equation by using variable substitution.Secondly,by designing the controller of the error system,it is proved that the drive system and the response system can achieve finite-time synchronization under the controller.Finally,based on the theoretical analysis results above,we give some examples of numerical simulations,which verify the correctness and effectiveness of the theoretical analysis.Later,we studied the finite-time synchronization problem of the second kind of fuzzy inertia neutral neural network.Firstly,we established the drive response system model of fuzzy delayed inertial neutral neural network.We did not use the variables of the original system to obtain differential equations,but directly analyzed the original system(this is a difference between this paper and the previous paper).Secondly,we proved that the drive system and the response system could achieve finite-time synchronization by designing the controller of the error system.To verify the effectiveness of the theoretical analysis,we give some examples of numerical simulations finite time synchronization.Finally,the main research contents of this paper are summarized and the future research directions of delayed inertial neural networks are determined.