Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, Manauli, 140306, India.
Sci Rep. 2021 Oct 22;11(1):20913. doi: 10.1038/s41598-021-00174-0.
We consider the dynamics of a three-species system incorporating the Allee Effect, focussing on its influence on the emergence of extreme events in the system. First we find that under Allee effect the regular periodic dynamics changes to chaotic. Further, we find that the system exhibits unbounded growth in the vegetation population after a critical value of the Allee parameter. The most significant finding is the observation of a critical Allee parameter beyond which the probability of obtaining extreme events becomes non-zero for all three population densities. Though the emergence of extreme events in the predator population is not affected much by the Allee effect, the prey population shows a sharp increase in the probability of obtaining extreme events after a threshold value of the Allee parameter, and the vegetation population also yields extreme events for sufficiently strong Allee effect. Lastly we consider the influence of additive noise on extreme events. First, we find that noise tames the unbounded vegetation growth induced by Allee effect. More interestingly, we demonstrate that stochasticity drastically diminishes the probability of extreme events in all three populations. In fact for sufficiently high noise, we do not observe any more extreme events in the system. This suggests that noise can mitigate extreme events, and has potentially important bearing on the observability of extreme events in naturally occurring systems.
我们研究了包含阿利效应的三种群系统的动力学，重点研究了它对系统中极端事件出现的影响。首先，我们发现阿利效应下规则的周期动力学会转变为混沌。此外，我们发现系统在阿利参数的临界值之后，植被种群表现出无界的增长。最显著的发现是观察到一个临界阿利参数，超过这个参数，所有三种种群密度获得极端事件的概率都不为零。尽管捕食者种群中的极端事件的出现受阿利效应的影响不大，但在阿利参数的阈值之后，猎物种群获得极端事件的概率急剧增加，而植被种群在足够强的阿利效应下也会产生极端事件。最后，我们考虑了加性噪声对极端事件的影响。首先，我们发现噪声可以驯服阿利效应引起的无界植被增长。更有趣的是，我们证明了随机性极大地降低了所有三种群中极端事件的概率。事实上，对于足够高的噪声，我们在系统中不再观察到任何极端事件。这表明噪声可以减轻极端事件，并对自然发生系统中极端事件的可观测性具有潜在的重要影响。
