Persistence in mean and extinction of a hybrid stochastic delay Gompertz model with Levy jumps

This paper deals with a stochastic delay Gompertz model under regime switching with Levy jumps. Firstly, the existence of a unique global positive solution has been derived. Secondly, sufficient conditions for extinction and persistence in mean are obtained. Finally, an example is given to illustrate our main results.The results in this paper indicate that Levy jumps noise, the white noise and switching noise have certain effects on the properties of the model.

Keywords:

Gompertz model , persistence in mean , extinction , Levy jumps noise , Markov chains