| Memristor is considered to be the perfect device for simulating synapse,and the artificial neural network using memristor to simulate synapse is called memristor-based neural network.Synchronization is an important dynamic behavior in neural networks,and neural networks can achieve many kinds of synchronization under the appropriate controller.Memristor-based neural networks and the synchronization control of memristor-based neural networks have important applications in many fields,including the cooperative control of intelligent robots,the prevention and treatment of mental disorders such as epilepsy,associative memory,human brain recognition,etc.Because memristor has the characteristic of pinched hysteresis loop,memristor-based neural networks often exhibit some special dynamic behaviors and can generate some new chaotic systems.Based on the dynamic behaviors of memristor-based neural network,memristor-based neural networks and the synchronization control of memristor-based neural networks can also be applied to secure communication,image encryption,pseudo-random number generator and other information security fields.This paper studies the adaptive synchronization of memristor-based neural networks,the finite-time synchronization of memristor-based neural networks,the fixed-time synchronization of memristor-based neural networks,and the applications of memristor-based neural network in secure communication and image encryption.The main works and innovations are as follows:1.The adaptive synchronization of memristor-based neural networks,which includes three works we have done.In the first work,by designing an adaptive controller,we prove the coupled memristor-based neural networks with mixed delays and stochastic perturbations can achieve asymptotic synchronization in mean square sense under the designed controller.In the proof,Ito formula and LaSalle invariant principle are also used.In the second work,by designing two double-layer adaptive controllers,we prove the studied memristor-based BAM neural networks with mixed delays can achieve asymptotic synchronization and exponential synchronization under the designed controllers.In the third work,by designing two adaptive controllers,we prove the memristor-based neural networks with mixed delays can achieve asymptotic lag synchronization and exponential lag synchronization under the designed controllers.The structure of memristor-based neural network with mixed delays is complex,so it is difficult to study the adaptive synchronization control of memristor-based neural networks with mixed delays.Only a few research results in this area were based on some strong assumptions,and the designed controllers were very complex.The studied memristor-based neural networks in our three works all have mixed delays,and the studied memristor-based BAM neural network has a complex two-layer connection structure.However,the adaptive controllers that we design are very simple,and the assumptions that we use are weak.In our three works,we adopt some special analysis methods.First we obtain several lemmas,which can effectively simplify the theoretical derivations and make the relevant proof process very simple.The numerical simulation results show the designed adaptive controllers have small control gains.2.The finite-time synchronization of memristor-based neural networks,which includes two works we have done.In the first work,by designing a feedback controller and using a new finite-time synchronization analysis method,we obtain a finite-time synchronization criterion for ordinary memristor-based neural networks with mixed delays.In the second work,by designing a feedback controller and using a new finite-time synchronization analysis method,we obtain a finite-time synchronization criterion for memristor-based Cohen-Grossberg neural networks with mixed delays.Because memristor-based Cohen-Grossberg neural network has amplification function,we first introduce a transformation function to transform memristor-based Cohen-Grossberg neural network into an ordinary memristor-based neural network,and then do analysis by using the similar analysis methods as those in the first work.Previous research results on the finite-time synchronization of memristor-based neural networks were based on a popular finite-time synchronization analysis method,which was more suitable for studying simple memristor-based neural networks.If the studied memristor-based neural networks contain mixed delay,the popular finite-time synchronization analysis method requires the designed controllers are very complex.In the two works we have done,the studied memristor-based neural networks have mixed delays.However,because a new finite-time synchronization analysis method is adopted,only very simple controllers are needed.The numerical simulation results show that the control effect of the designed feedback controllers is very good.3.The fixed-time synchronization of memristor-based neural networks,which includes two works we have done.In the first work,by designing a two-layer feedback controller,we obtain a fixed-time synchronization criterion for memristor-based BAM neural networks with discrete delay.Up to now,fixed-time synchronization is still a new research topic.Especially,the research results about the fixed-time synchronization of memristor-based neural networks are very few.The structure of memristor-based BAM neural network is very complex,so it is more difficult to study the fixed-time synchronization of memristor-based BAM neural networks.In this paper,the fixed-time synchronization of memristor-based BAM neural networks is studied for the first time.In the proof,we adopt some special analysis methods.First we obtain four lemmas,which can effectively simplify the theoretical derivations and solve the complex connection structure problem of memristor-based BAM neural network.In the second work,by designing four double-layer feedback controllers,we obtain four fixed-time synchronization criteria of inertial memristor-based neural networks with discrete delay.First a variable substitution is introduced to transform the second-order differential equation representing inertial memristor-based neural network into two first-order differential equations.Since these two first-order differential equations have similar form to memristor-based BAM neural network,analysis methods similar to those in the first work can be used next.The numerical simulation results verify the validity of the theoretical results.4.The applications of memristor-based neural network in secure communication and image encryption,which includes two works we have done.In the first work,based on the dynamic behaviors and synchronization control of memristor-based neural networks,a secure communication scheme is proposed,and the effectiveness of the secure communication scheme is theoretically proved and verified by numerical simulations.In the second work,based on the dynamic behaviors of memristor-based Cohen-Grossberg neural network,an image encryption scheme is proposed,and the effectiveness of the image encryption scheme is verified by numerical simulations.In addition,the security analysis of the image encryption scheme is also given.Because memristor has the characteristic of pinched hysteresis loop,memristor-based neural networks often exhibit some special dynamic behaviors and can generate some new chaotic systems.In fact,secure communication and image encryption can be studied by using the dynamic behaviors and synchronization control of memristor-based neural networks.However,the related research results are very rare at present.Only a few research results were based on memristor-based multi-directional associative memory neural network and other complex memristor-based neural networks.In our two works,the memristor-based neural network and memristor-based Cohen-Grossberg neural network are both simple and easy to implement.The research results in this part are expected to provide a new perspective for studying secure communication and image encryption. |
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