# American Institute of Mathematical Sciences

March  2015, 20(2): 683-701. doi: 10.3934/dcdsb.2015.20.683

## Optimal harvesting for a stochastic N-dimensional competitive Lotka-Volterra model with jumps

 1 Department of Mathematics, Harbin Institute of Technology, Weihai 264209 2 Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209

Received  January 2014 Revised  August 2014 Published  January 2015

Optimization problem for a stochastic N-dimensional competitive Lotka-Volterra system is studied in this paper. The considered system is driven by both white noise and jumping noise, and the jumping noise is modeled by a stochastic integral with respect to a Poisson counting measure generated by a Poisson point process. For two types of objective functions, namely, time-averaged yield and sustained yield, the optimal harvesting efforts as well as the corresponding maximum yields are given respectively. Moreover, almost sure equivalence between these two objective functions is proved by ergodic method. This paper provides us a new idea to study the stochastic optimal harvesting problem with sustained yield, and this idea can be popularized to other stochastic systems.
Citation: Xiaoling Zou, Ke Wang. Optimal harvesting for a stochastic N-dimensional competitive Lotka-Volterra model with jumps. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 683-701. doi: 10.3934/dcdsb.2015.20.683
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