Bio-economics of a renewable resource in a seasonally varying environment. (English) Zbl 1106.92063

Castilho, César; Srinivasu, Pichika D. N.

Math. Biosci. 205, No. 1, 1-18 (2007).

Summary: We study the bio-economics of a renewable resource with governing dynamics described by two distinct growth functions (viz., logistic and Gompertz growth functions) in a seasonally varying environment. Seasonality is introduced into the system by taking the involved ecological parameters to be periodic. We establish a procedure to obtain the optimal path and compute the optimal effort policy which maximizes the net revenue to the harvester for a fairly general optimal control problem and apply this procedure to the considered models to derive some important conclusions.
These problems are solved on the infinite horizon. We find that, for both the models, the optimal harvest policy and the corresponding optimal path are periodic after a finite time. We also obtain an optimal solution, a suboptimal harvesting policy and the corresponding suboptimal approach path to reach this optimal solution. The key results are illustrated using numerical simulations and we compare the revenues to the harvester along the optimal and suboptimal paths. The general procedure developed in this work, for obtaining the optimal effort policy and the optimal path, has wider applicability.

MSC:

92D40	Ecology
91B76	Environmental economics (natural resource models, harvesting, pollution, etc.)
49N90	Applications of optimal control and differential games
34C25	Periodic solutions to ordinary differential equations

Keywords:

bio-economics; optimal harvest policy; periodic solutions

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