In this paper, the deterministic and stochastic SIRS epidemic models with nonlinear incidence are introduced and investigated. For deterministic system, the basic reproductive number R0 is obtained. Furthermore, if R0≤1, then the disease-free equilibrium is globally asymptotically stable and...

In this paper, we study a stochastic predator–prey model with Beddington–DeAngelis type functional response and logistic growth for predators. The deterministic model is already well-studied and we recall some important results here. We construct the stochastic model from the deterministic...

The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of “disorder” when the observed process changes its probability characteristics. We give a partial answer to this question for some special cases of Lévy processes and present a...

We prove an Itô’s formula for Walsh’s Brownian motion in the plane with angles according to a probability measure μ on [0,2π[. This extends Freidlin–Sheu formula which corresponds to the case where μ has finite support. We also give some applications.

In this paper, a stochastic Lotka–Volterra competitive model with time-dependent delays is investigated. Sufficient conditions for global asymptotic stability of the positive equilibrium are established. The obtained result demonstrates that time-dependent delays have important impacts on the...

Since switching systems are important in research and industry, the article is concerned about the stabilization of fractional order switching systems with the order of 1 q 2 and a time delay actuator. To this end, the so-called system was initially converted to a system with no delay using a...

In this paper the existence and stability of equilibriums in an evolutionary game theory model of the labour market is studied by using the Lyapunov method. The model displays multiple equilibriums and it is shown that the Nash equilibriums of the static game are evolutionary stable equilibrium...

In this paper, we study the structure of trajectories of discrete disperse dynamical systems with a Lyapunov function which are generated by set-valued mappings. We establish a weak version of the turnpike property which holds for all trajectories of such dynamical systems which are of a...