Coexistence and harvesting optimal policy in three species food chain model with general Holling type functional response. (29th June 2021)

• Record Type: Journal Article
• Authors: Dawed, Mohammed Y.; Kebedow, Kiros G.
• Other Names: Blackwood Julie guestEditor.; Robertson Suzanne guestEditor.
• Is Part Of: Natural resource modelling. Volume 34:Number 3(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-06-29
• Subjects: bionomic equilibrium -- equilibrium point -- Holling type response functions -- Liapunov function -- maximal net revenue -- optimal harvesting policy -- persistence; Conservation of natural resources -- Mathematical models -- Periodicals; Ecology -- Mathematical models -- Periodicals; 371.397
• DOI: 10.1111/nrm.12316
• Languages: English
• ISSNs: 0890-8575

Abstract

Abstract: In this paper, we have discussed harvesting of prey and intermediate predator species. Both are subjected to Holling type I–V functional response. Conditions for local and global stability of the nonnegative equilibria are verified. The permanent coexistence criterion of the model system and existence of optimal equilibrium solution of the control problem are demonstrated. Maximum sustainable yield and maximal net present revenue are determined. To confirm analytical results, numerical solution has been carried out using the Matlab™ ODE solver ODE45 and the simulations show the model system reveals complex behavior (such as oscillations), which reflects the real situation. Recommendations for Resource Managers From our investigation of this study, we recommend to the management the following points. 1. Coexistence of the three species with harvesting, or persistence of the model system is possible provided that good management(treatment) of some factors (such as harvesting rate, growth rate of species, etc.) are performed. 2. The dynamics reveals complex behavior (such as oscillations), which reflects the real situation and it is sensitive to the above factors, especially the growth rate of the intermediate predator. 3. The policy makers should recommend the optimal effort h * to be applied and the optimal stock ( x *, y *, z * ) to harvest. This indicates that maximum profit will attain while securing sustainability of the three species in the ecosystem.