Optimal exploitation of a periodic Gompertz equation with random fluctuations

Taking white noise, Lévy jumps, and periodic factors in the environments into account, we formulated a periodic stochastic Gompertz model with impulsive harvesting and investigated its optimal impulsive exploitation problem. For periodic stochastic ecosystems with Lévy jumps and impulsive harvesting, two traditional approaches, the Fokker-Planck equation approach and ergodicity-based approach used to study the optimal exploitation problems were invalid because for almost all such ecosystems, one could not solve the associated Fokker-Planck equations. In addition, the ecosystems have no traditional non-boundary invariant measures. The present study utilized a different method. By exploring the associated Hamilton function, we derived an optimal exploitation strategy. An example was also introduced to illustrate the theoretical results.