Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment

2017 ◽  
Vol 477 ◽  
pp. 20-33 ◽  
Author(s):  
Yu Zhao ◽  
Sanling Yuan
Keyword(s):  
Lévy Noise ◽  
Optimal Harvesting ◽  
Polluted Environment ◽  
Optimal Harvesting Policy ◽  
Competitive Model ◽  
Levy Noise

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.

scholarly journals An Enhanced Intrinsic Time-Scale Decomposition Method Based on Adaptive Lévy Noise and Its Application in Bearing Fault Diagnosis

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 617
Author(s):  
Jianpeng Ma ◽  
Shi Zhuo ◽  
Chengwei Li ◽  
Liwei Zhan ◽  
Guangzhu Zhang
Keyword(s):  
Fault Diagnosis ◽  
Time Scale ◽  
Lévy Noise ◽  
Model Parameters ◽  
Rolling Bearings ◽  
Intrinsic Time ◽  
Time Scale Decomposition ◽  
Weak Fault ◽  
Levy Noise ◽  
The Impact

When early failures in rolling bearings occur, we need to be able to extract weak fault characteristic frequencies under the influence of strong noise and then perform fault diagnosis. Therefore, a new method is proposed: complete ensemble intrinsic time-scale decomposition with adaptive Lévy noise (CEITDALN). This method solves the problem of the traditional complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN) method not being able to filter nonwhite noise in measured vibration signal noise. Therefore, in the method proposed in this paper, a noise model in the form of parameter-adjusted noise is used to replace traditional white noise. We used an optimization algorithm to adaptively adjust the model parameters, reducing the impact of nonwhite noise on the feature frequency extraction. The experimental results for the simulation and vibration signals of rolling bearings showed that the CEITDALN method could extract weak fault features more effectively than traditional methods.

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