This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment.The influence of environmental fluctuation is accommodated ...This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment.The influence of environmental fluctuation is accommodated by choosing the coefficients in the differential equation to be periodic functions with the same period and restriction on the harvesting effort is accommodated by considering binding constraints on the control variable.Hence,a linear optimal control problem has been considered where the state dynamics is governed by Gompertz equation and the control variable is subject to the binding constraints.With the help of maximum principle and the concept of blocked intervals,an optimal periodic solution has been obtained which is followed by the construe tion of optimal solution using the theory of most rapid approach.Important results of the study are demonstrated through numerical simulations.展开更多
文摘This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment.The influence of environmental fluctuation is accommodated by choosing the coefficients in the differential equation to be periodic functions with the same period and restriction on the harvesting effort is accommodated by considering binding constraints on the control variable.Hence,a linear optimal control problem has been considered where the state dynamics is governed by Gompertz equation and the control variable is subject to the binding constraints.With the help of maximum principle and the concept of blocked intervals,an optimal periodic solution has been obtained which is followed by the construe tion of optimal solution using the theory of most rapid approach.Important results of the study are demonstrated through numerical simulations.
