The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war, terrorism and others. First, adding random perturbations proportionally to each variable, we get the dy...The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war, terrorism and others. First, adding random perturbations proportionally to each variable, we get the dynamic properties around the positive equilibrium of the deterministic model and the conditions for persistence and extinction. Second, giving a random disturbance to endemic equilibrium, we get a stochastic system with jumps. By modifying the existing Lyapunov function, we prove the positive solution of the system is stochastically stable.展开更多
基金partially supported by the Natural Science Foundation of Heilongjiang Province(A201420)Educational Reform Project of Heilongjiang Province(JG2013010482)+1 种基金Foundation of Heilongjiang Province Educational Committee(12541696)the Natural Science Foundation of China(11401136,11301112,11301207,11501148)
文摘The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war, terrorism and others. First, adding random perturbations proportionally to each variable, we get the dynamic properties around the positive equilibrium of the deterministic model and the conditions for persistence and extinction. Second, giving a random disturbance to endemic equilibrium, we get a stochastic system with jumps. By modifying the existing Lyapunov function, we prove the positive solution of the system is stochastically stable.
