Mean First Passage Time and Escape Rate of Improved Predator-Prey Model with Color-Correlated Gaussian Noise
1. School of Computer and Mathematics, Yuzhang Normal University, Nanchang 330103, China
2. School of Aeronautical Mechanical and Electrical Engineering, Jiangxi Flight University, Nanchang 330088, China
| Abstract: | Changing the initial state of a population has been proven to have profound impacts on the dynamics of the system and the long-term sustainability of species. Relevant studies have revealed the sensitivity of system parameters, providing a new perspective on system dynamics. The steady-state probability distribution function, mean first passage time and escape rate are obtained by theoretical calculation to discuss the effects of system parameters on the statistical properties of the improved predator-prey model. Obtained results show that the peak of the steady-state probability distribution function decreases with the increase of the multiplicative noise intensity, and its peak decreases with the increase of the birth rate related parameter, and the peak gradually shifts to the right. However, the peak of steady-state probability distribution function gradually becomes larger and more obvious when the correlation strength between noise increases. The mean first passage time T+(x-→xu) and T-(x+→xu) both show a trend of increasing first and then decreasing with the increase of additive noise intensity, but T-(x+→xu) changes faster. With the increase of multiplicative noise intensity, T+(x-→xu) shows a non-monotonic behavior of rapid rise and slow decline, while T-(x+→xu) shows a trend of rising first and then declining, with roughly the same speed of rising and falling. The escape rate W(x±→xu) shows a monotonically decreasing trend with the noise correlation strength, while its function image with the noise intensity shows a monotonically increasing trend. Above results can provide some theoretical guidance for the protection of endangered species from the perspective of statistical physics to ensure that biodiversity conservation is carried out more effectively. |
| Keywords: | Color Correlation Noise; Predator and Prey; Environmental Effect; Mean First Passage Time; Escape Rate |
| DOI: | 10.57237/j.wjms.2025.02.004 |
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Received: 30 September 2025
Accepted: 3 December 2025
Published Online: 29 December 2025
Funding
| 1. | College Student Innovation Training Program Project of Yuzhang Normal University (Grant No. YZCXCY2024048) |
| 2. | Natural Science Foundation of Jiangxi Provincial (Grant No. 20232BAB201048) |
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