Periodic Solution and Ergodic Stationary Distribution of Stochastic SIRI Epidemic Systems with Nonlinear Perturbations

2019 ◽  
Vol 32 (4) ◽  
pp. 1104-1124 ◽  
Author(s):  
Weiwei Zhang ◽  
Xinzhu Meng ◽  
Yulin Dong
Keyword(s):  
Periodic Solution ◽  
Stationary Distribution ◽  
Nonlinear Perturbations

scholarly journals Long-time behaviors of two stochastic mussel-algae models

2021 ◽  
Vol 18 (6) ◽  
pp. 8392-8414
Author(s):  
Dengxia Zhou ◽  
◽  
Meng Liu ◽  
Ke Qi ◽  
Zhijun Liu ◽  
...  
Keyword(s):  
Periodic Solution ◽  
Stationary Distribution ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
The Other ◽  
Environmental Perturbations ◽  
Periodic Model ◽  
Long Time ◽  
The Mean

<abstract><p>In this paper, we develop two stochastic mussel-algae models: one is autonomous and the other is periodic. For the autonomous model, we provide sufficient conditions for the extinction, nonpersistent in the mean and weak persistence, and demonstrate that the model possesses a unique ergodic stationary distribution by constructing some suitable Lyapunov functions. For the periodic model, we testify that it has a periodic solution. The theoretical findings are also applied to practice to dissect the effects of environmental perturbations on the growth of mussel.</p></abstract>

Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems

2018 ◽  
Vol 508 ◽  
pp. 223-241 ◽  
Author(s):  
Haokun Qi ◽  
Shengqiang Zhang ◽  
Xinzhu Meng ◽  
Huanhe Dong
Keyword(s):  
Periodic Solution ◽  
Stationary Distribution

scholarly journals Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Chunjin Wei ◽  
Yingjie Fu
Keyword(s):  
Periodic Solution ◽  
White Noise ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Population Extinction ◽  
Persistence In The Mean ◽  
Existence And Stability ◽  
Globally Positive Solution ◽  
The Stability

In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations.

Periodic solution and stationary distribution of stochastic S-DI-A epidemic models

2016 ◽  
Vol 97 (2) ◽  
pp. 179-193 ◽  
Author(s):  
Xinhong Zhang ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Periodic Solution ◽  
Stationary Distribution ◽  
Epidemic Models

scholarly journals Periodic solution and stationary distribution for stochastic predator-prey model with modified Leslie-Gower and Holling type II schemes

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1383-1402
Author(s):  
Qixing Han ◽  
Liang Chen ◽  
Daqing Jiang
Keyword(s):  
Periodic Solution ◽  
Computer Simulations ◽  
Stationary Distribution ◽  
Autonomous System ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Autonomous Case

In this paper, a stochastic predator-prey system with modified Leslie-Gower and Holling type II schemes is studied. For the autonomous case, we prove that the system has a stationary distribution under some parametric restrictions. We also obtain conditions for the non-persistence of the system, and the results are illustrated by computer simulations. For the non-autonomous system with continuous periodic coefficients, sufficient conditions which guarantee the existence of periodic solution of the system are established.

Sign in / Sign up

Export Citation Format

Share Document