Optimal harvesting problems for an age-dependent n-dimensional food chain model with diffusion

2007 ◽  
Vol 184 (2) ◽  
pp. 659-668
Author(s):  
Dianchen Lu ◽  
Jianjun Gu ◽  
Xiaoming wang
Keyword(s):  
Food Chain ◽  
Optimal Harvesting ◽  
Chain Model ◽  
Age Dependent ◽  
Food Chain Model

OVERTAKING OPTIMAL HARVESTING FOR AN AGE-DEPENDENT n-DIMENSIONAL FOOD CHAIN MODEL

2013 ◽  
Vol 06 (04) ◽  
pp. 1350024
Author(s):  
ZHIXUE LUO ◽  
HUI ZHANG ◽  
YONGCHENG ZHANG
Keyword(s):  
Maximum Principle ◽  
Food Chain ◽  
Infinite Horizon ◽  
Optimal Trajectories ◽  
Optimal Harvesting ◽  
Chain Model ◽  
Controlled System ◽  
Age Dependent ◽  
Food Chain Model

This paper is concerned with an optimal harvesting problem over an infinite horizon for age-dependent n-dimensional food chain model and the analysis of long-term behaviors of the optimal-controlled system. The existence of overtaking optimal policy is proved and a maximum principle is carefully derived by means of Dubovitskii–Milyutin functional analytical extremum theory. Weak and strong turnpike properties of optimal trajectories are established.

Food chain model with optimal harvesting in fuzzy environment

2009 ◽  
Vol 34 (1-2) ◽  
pp. 1-18 ◽  
Author(s):  
D. Sadhukhan ◽  
L. N. Sahoo ◽  
B. Mondal ◽  
M. Maiti
Keyword(s):  
Food Chain ◽  
Optimal Harvesting ◽  
Chain Model ◽  
Fuzzy Environment ◽  
Food Chain Model

Effects of Additional Food on the Dynamics of a Three Species Food Chain Model Incorporating Refuge and Harvesting

2019 ◽  
Vol 20 (7-8) ◽  
pp. 787-801
Author(s):  
Prabir Panja ◽  
Soovoojeet Jana ◽  
Shyamal Kumar Mondal
Keyword(s):  
Growth Rate ◽  
Food Chain ◽  
Carrying Capacity ◽  
Rate Increase ◽  
Optimal Harvesting ◽  
Chain Model ◽  
Predator Population ◽  
Intrinsic Growth Rate ◽  
Additional Food ◽  
Food Chain Model

AbstractIn this paper, a three species food chain model has been developed among the interaction of prey, predator and super predator. It is assumed that the predator shows refuge behavior to the super predator. It is also assumed that a certain amount of additional food will be supplied to the super predator. It is considered that the predator population is benefiting partially from the additional food. To get optimal harvesting of super predator the Pontryagin’s maximum principle has been used. It is found that super predator may be extinct if harvesting rate increase. It is observed that as the refuge rate increases, predator population gradually increases, but super predator population decreases. Also, it is found that our proposed system undergoes oscillatory or periodic behavior as the value of refuge rate (m1), harvesting rate (E), the intrinsic growth rate of prey (r), carrying capacity of prey (k) and conservation rate of prey (c1) varies for some certain range of these parameters. It is found that this study may be useful for the increase of harvesting of a super predator by supplying the additional food to our proposed system.

scholarly journals Dynamic analysis of a stochastic four species food-chain model with harvesting and distributed delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nafeisha Tuerxun ◽  
Zhidong Teng ◽  
Wei Chen
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Probability Distribution ◽  
Food Chain ◽  
Distributed Delay ◽  
Optimal Harvesting ◽  
Global Dynamics ◽  
Chain Model ◽  
Ultimate Boundedness ◽  
Food Chain Model

AbstractA stochastic four species food-chain model is proposed in this paper. Here, artificial harvest in each species and the effect of time delay for interaction between species are considered, which makes the model more applicable in real situations. Specifically, we address the stochastic global dynamics behavior, including the existence of global positive solutions, stochastic ultimate boundedness, extinction with probability one, persistence in mean and global stability. The asymptotic stability in the probability distribution is obtained, and the criterion for the existence and non-existence of the optimal harvesting strategy is also derived. Furthermore, this paper can provide reference for the research of general n-species stochastic food-chain models.

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