Convergence Behavior Of Coupled Dynamical Systems With Delays

Coupled dynamic systems are widely used to depict many phenomena in the real world.More and more attention has been paid to the complexity of their network structures and the diversity of their dynamic behaviors.The convergence of coupled dynamic systems is one of the important contents of its dynamic behavior research.The related research results have been widely used in the fields of artificial intelligence,biotechnology,communication security and social networks.In recent years,a lot of achievements have been made in the study of convergence behavior of coupled dynamic systems.It is worth noting that the research on the complexity of the spatial structure of coupling network and the energy cost in the process of convergence is not deep enough,and many key problems have not been solved.Based on this,this paper mainly focuses on these problems.The synchronization of reaction-diffusion coupled neural networks with impulsive effect and hybrid coupling structure is studied.In the coupled network model,the effects of impulse effect and spatial diffusion coupling structure are considered simultaneously,which extends the comprehensiveness and practicability of the model.Aiming at the synchronization error network model,the accurate estimation of synchronization error state is realized by using the characteristics of reaction-diffusion coupling structure,the constant variation formula and the comparison principle of delay differential system.Combined with the average pulse interval technique,a unified synchronization criterion for two kinds of different pulse effects is established,which weakens the conservatism of the existing results.Finally,numerical examples and simulation experiments verify the effectiveness of the theoretical results.The guaranteed cost consistency of multi-agent systems with time-varying uncertain parameters is studied.The uncertainty of model parameters is introduced into the high-dimensional agent system,which expands the practical range of the model.In the process of consensus control,we construct the energy cost function according to the distributed characteristics of multi-agent system,combined with the relative error of agent and control input,which reflects the energy constraints of the system in the control process.By introducing a consensus protocol with distributed characteristics and input delay,using the properties of time-varying nonsingular transformation matrix and state space decomposition techniques,the sufficient conditions for agent systems to achieve cost consistency are given,and an upper bound of the cost function is given.Finally,numerical examples and simulation experiments show the correctness and effectiveness of the theoretical results.