| With the continuous development of neural networks technology,neural networks have been widely used in data processing,optimization design,pattern recognition and other fields,and is a research hot spot in artificial intelligence and control.Now it has become a global key research object.The time delay caused by the switching of amplifier is inevitable in the operation of neural networks,so it is more practical to study the neural networks with time delay.Different from constant delay,bounded time-varying delay and distributed delay,proportional delay is a kind of unbounded time-varying delay,which has been used in image compression and decryption and other fields.In this paper,we mainly discuss the global polynomial synchronization,global asymptotic synchronization and global polynomial stabilization of several kinds of neural networks with proportional delays.In Chapter 1,the development history of neural networks is described,and the research situations of non-proportional delayed neural networks,proportional delayed neural networks and proportional delayed inertial memristive neural networks are briefly introduced.In Chapter 2,the global polynomial synchronization of a class of proportional delayed neural networks as drive-response systems is studied.Firstly,through a nonlinear transformation,the proportional delayed neural networks are equivalently transformed into the neural networks with constant delays and time-varying coefficients.And then,the error system is obtained based on the transformed drive-response systems,and the exponential stability of the error system is studied by constructing Lyapunov functionals and applying the linear matrix inequality methods.Then the global polynomial synchronization of the original drive-response systems is obtained.Two criteria to ensure the global polynomial synchronization of the drive-response systems are obtained.Finally,the conclusion is verified by numerical examples and the simulations.In Chapter 3,it probes into the global asymptotic synchronization of neural networks,using a class of inertial memristive Cohen-Grossberg neural networks with proportional delays as driveresponse systems.By differential inclusion theory and appropriate variable transformation,the original drive-response systems can be converted to the first-order differential systems.Then,designing both feedback controller and adaptive controller,via constructing Lyapunov functionals,combining inequality techniques and a number of analysis methods,a few new judgments have been made in algebraic inequalities to ensure the global asymptotic synchronization of the systems.Finally,numerical examples and simulations are presented to verify the results.In Chapter 4,it probes into the global polynomial stabilization of a class of proportional delayed inertial memristive neural networks.Here,ruling out the reduced-order way,discusse the global polynomial stabilization of system under the second-order scheme directly.Firstly,a feedback controller is designed to make the system self-stabilizing.To farther save control expenses,employing an adaptive controller to make the system stabilized.By designing suitable Lyapunov functionals with adjustable parameters,combining with inequality techniques,two algebraic criteria are obtained to realize the global polynomial stabilization of system.Finally,two numerical examples which sustain the usability of the obtained theoretical conclusions are shown.The research results and methods obtained in this paper are novel and easy to verify.Each chapter gives numerical examples and simulations to verify the research results.The results can provide some theoretical support for the application research of proportional delayed neural networks. |
