Abstract
In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.
| Original language | English |
|---|---|
| Pages (from-to) | 191-212 |
| Number of pages | 22 |
| Journal | Stochastic Analysis and Applications |
| Volume | 38 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 3 Mar 2020 |
| Externally published | Yes |
Keywords
- Brownian motion
- Markov chain
- Stochastic predator–prey model
- time delay
- ultimate boundedness
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics
