Stabilization And Antisynchronization Of Memristive Neural Networks With Mixed Delays

Artificial neural network is a new subject which is based on neuroanatomy and neurophysiology to simulate biological neural network.It has become a research hotspot in cognitive science,mathematical science,biological neurology and computer science.Memristive neural networks are very suitable for designing synapses of artificial neural networks,and they are of great significance in the next generation of human brain computers.In recent years,memristive neural networks have been widely concerned.Its dynamic behaviors such as stability,exponential stabilization,fixed-time stabilization,synchronization and anti-synchronization have been studied.However,few studies can be found on the dynamic behavior of memristive neural networks with mixed delays such as distributed delays and leakage delays.In this paper,the exponential stabilization and fixed-time stabilization of memristive neural networks with mixed delays are studied,and the anti-synchronization problem of memristive neural networks with distributed delays and leakage terms is also studied.The main tasks are as follows:1.We study a class of memristive neural networks with mixed delays,The existence and uniqueness of its equilibrium point is proven without the boundedness and initial value of the activation function,and a criterion to ensure its exponential stabilization under a sampled-data controller is obtained by constructing an appropriate Lyapunov function.Meanwhile,the fixed-time stabilization of memristive neural networks is also gotten by Lyapunov method.The obtained results extend and enhance some existing ones.2.The problem of anti-synchronization of memristive neural networks with both distributed delays and leakage delays is studied.By designing an appropriate Lyapunov function,the condition to ensure the anti-synchronization of the memristive networks are given under the appropriate controller.We use some numerical examples to verify the above results.