An analysis on the approximate controllability of neutral impulsive stochastic integrodifferential inclusions via resolvent operators.

This article focuses on the approximate controllability of impulsive neutral stochastic integrodifferential inclusions in Hilbert spaces. We used resolvent operators, fixed point approaches, and semigroup theory to achieve the article's main results. First, we focus on the existence of approximate controllability, and we develop the existence results with nonlocal conditions. At last, an application is provided to illustrate the concept.

Stationary distribution and global stability of stochastic predator-prey model with disease in prey population.

In this paper, a new stochastic four-species predator-prey model with disease in the first prey is proposed and studied. First, we present the stochastic model with some biological assumptions and establish the existence of globally positive solutions. Moreover, a condition for species to be permanent and extinction is provided. The above properties can help to save the dangered population in the ecosystem. Through Lyapunov functions, we discuss the asymptotic stability of a positive equilibrium solution for our model. Furthermore, it is also shown that the system has a stationary distribution and indicating the existence of a stable biotic community. Finally, our results of the proposed model have revealed the effect of random fluctuations on the four species ecosystem when adding the alternative food sources for the predator population. To illustrate our theoretical findings, some numerical simulations are presented.

Finite-time decentralized non-fragile dissipative control for large-scale systems against actuator saturation.

This paper employs linear matrix inequality-based optimization algorithm to establish finite-time boundedness and dissipativeness for a class of large-scale systems in the presence of actuator faults and actuator saturation. In addition, for the proposed system, a novel time-varying actuator fault model is incorporated in controller design, which is more general than the conventional actuator fault models. Specifically, by constructing a suitable Lyapunov-Krasovskii functional, a new set of sufficient conditions is derived, which ensures the finite-time boundedness with dissipativity of the considered large-scale systems. The main intention of this paper is to design a novel decentralized fault-tolerant controller to compensate simultaneously the actuator faults, actuator saturations and nonlinear interconnections. Finally, an example and its simulation study are presented to verify the effectiveness and potential of the proposed control design technique.

Modeling the Dependency Structure of Integrated Intensity Processes.

This paper studies an important issue of dependence structure. To model this structure, the intensities within the Cox processes are driven by dependent shot noise processes, where jumps occur simultaneously and their sizes are correlated. The joint survival probability of the integrated intensities is explicitly obtained from the copula with exponential marginal distributions. Subsequently, this result can provide a very useful guide for credit risk management.