Stability of a Class of Hybrid Neutral Stochastic Differential Equations with Unbounded Delay

This paper studies the stability of hybrid neutral stochastic differential equations with unbounded delay. Some novel exponential stability criteria and boundedness conditions are established based on the generalized Itô formula and Lyapunov functions. The factor e-εδ(t) is used to overcome the difficulties caused by the unbounded delay δ(t) effectively. In particular, our results generalize and improve some previous stability results from bounded delay to unbounded delay conditions. Finally, an example is presented to demonstrate the effectiveness of the proposed results.

Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction

This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Finally, an example is given to illustrate the main results.

Stochastic Delay Logistic Model under Regime Switching

This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue ofV-function technique,M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.