Synchronization Analysis Of Inertial Memristive Neural Networks With Time-varying Delays

Synchronization,a common phenomenon in the nature,widely exists in the field of physics,chemistry,biology,engineering,society and economic science,et al.In recent years,synchronization of neural networks has been a hot topic and received much attention all around the world.Research on this topic is not only of great theoretical value but also of practical value.Investigation the syn-chronization of neural network can help us have a better understanding of the collective behavior of networks,explain many phenomena in our daily life and guide the practise.Based on the Lyapunov functional method,matrix theory,Halanay inequality as well as control theory,this dissertation addresses the exponential synchronization,finite-time synchronization and fixed-time synchroniza-tion of inertial memristive neural networks.The dissertation is divided into four chapters and the organization is as follows.In the first chapter,the significance and development tendency of neural networks together with current research situation of inertial memristive neural networks are briefed.The main contents and the main contribution of this dissertation are also expounded according to the above mentioned analysis.The second chapter investigates the synchronization problem of inertial memristive neural net-works with time-varying delay.By using a variable transmission,the original system can be trans-formed into first-order differential equations.Then,by constructing Lyapunov functional and design-ing a feedback controller,several sufficient conditions are derived for complete synchronization of inertial memristive neural networks without parameter mismatch.We also consider the inertial memristive neural networks with parameter mismatch,in this case,complete synchronization can not be achieved due to parameter mismatch,so the concept of quasi-synchronization is introduced.Based on Halanay inequality and matrix measure method,several quasi-synchronization criteria for the in-ertial memristive neural networks with parameter mismatch are given.Finally,numerical simulations are given to demonstrate the effectiveness of our proposed results.The third chapter deals with finite-time synchronization and fixed-time synchronization prob-lems of inertial memristive neural networks with time-varying delay.The objection is to find under what condition the system error can reach zero in finite time.Based on a Lyapunov functional,several sufficient conditions for the finite-time synchronization of inertial memristive neural networks arc achieved by designing a feedback controller.Compared with finite-time synchronization where the convergence time relies on the initial synchronization error,the settling time of fixed-time syn-chronization can be adjusted to any expected values regardless of the initial synchronization error.An novel criteria to guarantee the fixed-time synchronization of inertial memristive neural networks can be achieved.Finally,two examples are provided to demonstrate the effectiveness of our main results.In the fourth chapter,the research work of this dissertation is summarized.Further more,the possible improved methods are proposed and the prospect for the future work is derived.