In this paper, the global exponential stability and periodicity for a class of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions are addressed by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential converge to 0 of the difference between any two solutions of the original reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions, the existence and uniqueness of equilibrium is the direct results of this procedure. This approach is different from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps. Furthermore, we prove periodicity of the reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Sufficient conditions ensuring the global exponential stability and the existence of periodic oscillatory solutions for the reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions are given. These conditions are easy to check and have important leading significance in the design and application of reaction–diffusion recurrent neural networks with delays. Finally, two numerical examples are given to show the effectiveness of the obtained results.

Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions

Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays

Global exponential stability of BAM neural networks with distributed delays and reaction–diffusion terms

Exponential stability of complex-valued neural networks with mixed delays

In this paper, the dissipativity of neural networks with both variable and unbounded delays is investigated. By constructing proper Lyapunov functions and using some analytic techniques, several sufficient conditions are given to ensure the dissipativity of neural networks with both variable and unbounded delays. The results extend and improve the earlier publication. An example is given to show the effectiveness of the obtained results.

Global dissipativity of neural networks with both variable and unbounded delays

Absolutely exponential stability of a class of neural networks with unbounded delay

An important aspect of an automated highway system design is the synthesis of an automated vehicle following system. Associated with automated vehicle following system is the problem of the stability of a string of vehicle, i.e., the problem of spacing error propagation, and in some cases, amplification upstream from one vehicle to another, due to some disturbance at the head of the string. In this paper, the novel method to determine the stability of a string of vehicle is established based on the vector Liapunov method. Based on the new results for the stability of string of vehicle, the controller is constructed by sliding mode control method. The stability domain of the controller parameters of the string of vehicles is enlarged.

Jiye Zhang

Papers

Absolutely exponential stability of a class of neural networks with unbounded delay

Vector Liapunov Function Approach to Longitudinal Control of Vehicles in a Platoon