This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both the pth moment and almost sure exponential stability criteria are established by using the average impulsive interval.When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it m...

Uncertain differential equation with jumps, as a crucial tool to deal with a discontinuous uncertain system, is a type of differential equation driven by both canonical Liu process and uncertain renewal process. So far, a concept of stability in measure for an uncertain differential equation with jumps has been proposed. As a supplement, this paper proposes a concept of almost sure stability fo...

This criterion theoretically requires the integration of the system equations until infinity. A possible way to overcome this impossible investigation is the approximation through an integration over a sufficiently long time interval as proposed in [1]. In the discussed paper the authors developed a criterion imposing that the system is averagely normcontractive over a finite time interval. Thi...

Almost sure asymptotic stability of stochastic difference and differential equations with non-anticipating memory terms is studied in R. Sufficient criteria are obtained with help of Lyapunov-Krasovskǐi-type functionals, martingale decomposition and semi-martingale convergence theorems. The results allow numerical methods for stochastic differential equations with memory to be studied in terms ...

We define Almost Sure Productivity (ASP), a probabilistic generalization of the productivity condition for coinductively defined structures. Intuitively, a probabilistic coinductive stream or tree is ASP if it produces infinitely many outputs with probability 1. Formally, we define almost sure productivity using a final coalgebra semantics of programs inspired from Kerstan and König. Then, we i...

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffu...

The aim of this paper is to argue that models in cognitive science based on probabilistic computation should not be restricted to those procedures that almost surely (with probability 1) terminate. There are several reasons to consider nonterminating procedures as candidate components of cognitive models. One theoretical reason is that there is a perfect correspondence between the enumerable se...