Wang Kang-Kang, Ye Hui, Wang Ya-Jun, Li Sheng-Hong
School of Science, Jiangsu University of Science and Technology, 212003, Zhenjiang, China.
School of Automation Engineering, Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, China.
Eur Phys J E Soft Matter. 2018 May 14;41(5):60. doi: 10.1140/epje/i2018-11668-9.
In this paper, the modified potential function, the stationary probability distribution function (SPDF), the mean growth time and the mean degeneration time for a vegetation growth system with time delay are investigated, where the vegetation system is assumed to be disturbed by cross-correlated multiplicative and additive noises. The results reveal some fact that the multiplicative and additive noises can both reduce the stability and speed up the decline of the vegetation system, while the strength of the noise correlation and time delay can both enhance the stability of the vegetation and slow down the depression process of the ecological system. On the other hand, with regard to the impacts of noises and time delay on the mean development and degeneration processes of the ecological system, it is discovered that 1) in the development process of the vegetation population, the increase of the noise correlation strength and time delay will restrain the regime shift from the barren state to the boom one, while the increase of the additive noise can lead to the fast regime shift from the barren state to the boom one. 2) Conversely, in the depression process of the ecological system, the increase of the strength of the correlation noise and time delay will prevent the regime shift from the boom state to the barren one. Comparatively, the increase of the additive and multiplicative noises can accelerate the regime shift from the boom state to the barren state.
本文研究了具有时滞的植被生长系统的修正势函数、平稳概率分布函数（SPDF）、平均生长时间和平均退化时间，其中假设植被系统受到交叉相关乘性噪声和加性噪声的干扰。结果揭示了这样一个事实，即乘性噪声和加性噪声都会降低植被系统的稳定性并加速其衰退，而噪声相关性强度和时滞都可以增强植被的稳定性并减缓生态系统的衰退过程。另一方面，关于噪声和时滞对生态系统平均发展和退化过程的影响，发现：1）在植被种群的发展过程中，噪声相关性强度和时滞的增加会抑制从贫瘠状态到繁荣状态的状态转变，而加性噪声的增加会导致从贫瘠状态到繁荣状态的快速状态转变。2）相反，在生态系统的衰退过程中，相关噪声强度和时滞的增加会阻止从繁荣状态到贫瘠状态的状态转变。相比之下，加性噪声和乘性噪声的增加会加速从繁荣状态到贫瘠状态的状态转变。
