Department of Mathematics, University of California, Davis, CA, 95616, USA.
Department of Environmental Science and Policy, University of California, Davis, CA, 95616, USA.
Bull Math Biol. 2022 Aug 14;84(9):102. doi: 10.1007/s11538-022-01059-7.
During recent years, the study of long transients has been expanded in ecological theory to account for shifts in long-term behavior of ecological systems. These long transients may lead to regime shifts between alternative states that resemble the dynamics of alternative stable states for a prolonged period of time. One dynamic that potentially leads to long transients is the group defense of a resource in a consumer-resource interaction. Furthermore, time lags in the population caused by discrete reproductive pulses have the potential to produce long transients, either independently or in conjunction to the transients caused by the group defense. In this work, we analyze the potential for long transients in a model for a consumer-resource system in which the resource exhibits group defense and reproduces in discrete reproductive pulses. This system exhibits crawl-by transients near the extinction and carrying capacity states of resource, and a transcritical bifurcation, under which a ghost limit cycle appears. We estimate the transient time of our system from these transients using perturbation theory. This work advances an understanding of how systems shift between alternate states and their duration of staying in a given regime and what ecological dynamics may lead to long transients.
近年来，生态理论中的长暂态研究已经扩展，以解释生态系统长期行为的变化。这些长暂态可能导致替代状态之间的状态转变，这种转变类似于替代稳定状态的动态，可以持续很长一段时间。一种潜在导致长暂态的动态是在消费者-资源相互作用中对资源的群体防御。此外，由于离散繁殖脉冲引起的种群时滞有可能产生长暂态，无论是独立的还是与群体防御引起的暂态相结合。在这项工作中，我们分析了一个具有群体防御和离散繁殖脉冲的消费者-资源系统模型中长暂态的可能性。该系统在资源的灭绝和承载能力状态附近表现出爬行暂态，以及在跨越临界点时出现幽灵极限环。我们使用摄动理论从这些暂态中估计我们系统的暂态时间。这项工作增进了对系统如何在替代状态之间转变以及它们在给定状态下停留的时间以及哪些生态动态可能导致长暂态的理解。
