@article{Ji2025, 
author = {Weiming Ji and Meng Liu},
title = {Optimal exploitation of a periodic Gompertz equation with random fluctuations},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {18770-18783},
keywords = {optimal exploitation, random environments, impulsive, periodic coefficients},
url = {https://www.sciopen.com/article/10.3934/math.2025838},
doi = {10.3934/math.2025838},
abstract = {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.}
}