Pal Krishnendu, Deb Smita, Dutta Partha Sharathi
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India.
Department of Chemistry, National Institute of Technology, Durgapur 713209, West Bengal, India.
Phys Rev E. 2022 Nov;106(5-1):054412. doi: 10.1103/PhysRevE.106.054412.
Complex spatial systems can experience critical transitions or tippings on crossing a threshold value in their response to stochastic perturbations. While previous studies have well characterized the impact of white noise on tipping, the effect of correlated noise in spatial ecosystems remains largely unexplored. Here, we investigate the effect of both multiplicative and additive Ornstein-Uhlenbeck (OU) correlated noise on the occurrence of critical transitions in spatial ecosystems. We find that decreasing the noise correlation time of OU (exponentially correlated) noise aggravates the chance of critical transitions in spatiotemporal ecological systems. Our results hold good and are supported by the analysis of three well-studied spatial ecological models of varying nonlinearity. We also compute spatial early warning indicators (e.g., spatial variance, spatial skewness, and spatial correlation) to determine their reliability in anticipating tipping points with variations in noise correlation. The indicators of critical transitions exhibit mixed success in forewarning the occurrence of a tipping point, as indicated by the distribution of Kendall's rank correlation.
复杂空间系统在对随机扰动的响应中，当越过阈值时可能会经历临界转变或突变。虽然先前的研究已经很好地描述了白噪声对突变的影响，但空间生态系统中相关噪声的影响在很大程度上仍未得到探索。在此，我们研究了乘性和加性奥恩斯坦 - 乌伦贝克（OU）相关噪声对空间生态系统中临界转变发生的影响。我们发现，降低OU（指数相关）噪声的噪声相关时间会增加时空生态系统中临界转变的可能性。我们的结果在对三个不同非线性程度的、经过充分研究的空间生态模型的分析中得到了验证和支持。我们还计算了空间早期预警指标（例如空间方差、空间偏度和空间相关性），以确定它们在预测噪声相关性变化时突变点的可靠性。如肯德尔等级相关性分布所示，临界转变指标在预警突变点的发生方面表现不一。
