Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching

2019 ◽  
Vol 536 ◽  
pp. 120893 ◽  
Author(s):  
Guodong Liu ◽  
Xinzhu Meng
Keyword(s):  
Regime Switching ◽  
Optimal Harvesting ◽  
Polluted Environment ◽  
Mutualism System

scholarly journals Dynamics and optimal harvesting of a stochastic predator-prey system with regime switching, S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 7 (3) ◽  
pp. 4068-4093
Author(s):  
Yuanfu Shao ◽  
Keyword(s):  
Regime Switching ◽  
Time Delays ◽  
Optimal Harvesting ◽  
Comparison Theory ◽  
Predator Prey ◽  
Prey System ◽  
Persistence In The Mean ◽  
Distributed Time Delays ◽  
Stability In Distribution ◽  
Lévy Jumps

<abstract><p>This work is concerned with a stochastic predator-prey system with S-type distributed time delays, regime switching and Lévy jumps. By use of the stochastic differential comparison theory and some inequality techniques, we study the extinction and persistence in the mean for each species, asymptotic stability in distribution and the optimal harvesting effort of the model. Then we present some simulation examples to illustrate the theoretical results and explore the effects of regime switching, distributed time delays and Lévy jumps on the dynamical behaviors, respectively.</p></abstract>

scholarly journals Optimal control for a size-structured predator-prey model in a polluted environment

2021 ◽  
Vol 269 ◽  
pp. 01004
Author(s):  
Tainian Zhang ◽  
Zhixue Luo
Keyword(s):  
Size Structure ◽  
Necessary Optimality Conditions ◽  
Optimal Harvesting ◽  
Polluted Environment ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Predator Prey Model ◽  
Dependent Model ◽  
The Fixed Point Theorem

In this paper, we deal with an optimal harvesting problem for a periodic predator-prey hybrid system dependent on size-structure in a polluted environment. In other words, a size-dependent model in an environment with a small toxicant content has been established. The well-posedness of state system is proved by using the fixed point theorem. The necessary optimality conditions are derived by tangent-normal cone technique in nonlinear functional analysis. The existence of a unique optimal harvesting policy is verified via the Ekeland’s variational principle. The optimal harvesting problem has an optimal harvesting policy, which has a Bang-Bang structure and provides a threshold for the optimal harvesting problem. Using the optimization theories and methods in mathematics to control phenomena of life. The objective function represents the total economic profit from the harvested population. Some theoretical results obtained in this paper provide a scientific theoretical basis for the practical application of the model.

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