Stability and convergence analysis for a class of neural networks

In this paper, we analyze and establish the stability and convergence of the dynamical system proposed by Xia and Feng, whose equilibria solve variational inequality and related problems. Under the pseudo-monotonicity and other conditions, this system is proved to be stable in the sense of Lyapunov and converges to one of its equilibrium points for any starting point. Meanwhile, the global exponential stability of this system is also shown under some mild conditions without the strong monotonicity of the mapping. The obtained results improve and correct some existing ones. The validity and performance of this system are demonstrated by some numerical examples.