Estimate of exponential convergence rate and exponential stability are studied for a class of neural networks which includes the Hopfield neural networks and the cellular neural networks. Both local and global exponential convergence is discussed. Theorems for estimate of exponential convergence rate are established and the bounds on the rate of convergence are given. The domains of attraction ...

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u′ t au t bu t . The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are ob...

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.

There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, where $c$ locally integrable any sign, $\tau(t)\leq t$ Lebesgue measurable, $\lim_{t\rightarrow\infty}\tau(t)=\infty$, we obtain sharp results, relating speed stability. We thus unify classical results Myshkis Lillo. also genera...

We study the stability of entropically regularized optimal transport with respect to marginals. Given marginals converging weakly, we establish a strong convergence for Schrödinger potentials, describing density couplings. When converge in total variation, couplings also variation. This is applied show that Sinkhorn’s algorithm converges variation when costs are quadratic and subgaussian or, mo...