Abstract
This paper deals with stochastic nonautonomous Gompertz model with Levy jumps. To begin with, the existence of a global positive solution and an explicit solution have been derived. In addition, asymptotic moment properties are discussed. Besides, sufficient conditions for extinction, persistence in mean, and weak persistence are obtained. It is proved that the variability of Levy jumps can affect the asymptotic property of the system.
Highlights
In mathematical ecology, the Gompertz model is one of the most important models, and it is considered to be one of best fitted to describe growth of certain types of tumor
The Gompertz model is another important type of mathematical models; for example, the growth of the industrial production, the life cycle of a product, and population growth over a certain period all comply with this model [ ]
In [ ], the authors assumed that the growth deceleration factor b did not change while the variability of environmental conditions induced fluctuations in the intrinsic growth rate a
Summary
The Gompertz model is one of the most important models, and it is considered to be one of best fitted to describe growth of certain types of tumor. X(t) satisfies the following equation: dX(t) = c(t) – a(t)X(t) dt + σ (t) dB(t) + ln + h(t, u) N(dt, du) on t ≥ with initial value X( ) = ln x , where c(t) is introduced in Assumption A. We show that the positive solution satisfies the following result if the jumpdiffusion coefficient is controlled under a certain range.
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