具有群体防御和非繁殖阶段的消费者-资源系统中长暂态的表征
Characterizing long transients in consumer-resource systems with group defense and nonreproductive stages
AI总结：
本研究构建了具备群体防御、离散繁殖脉冲特征的消费者-资源离散时间模型，识别出爬行式暂态与幽灵极限环等长暂态现象，用微扰理论估算暂态时间，推进了对生态系统状态转变及长暂态成因的理解。
摘要：
近年来，长暂态研究在生态学理论中得到拓展，用以解释生态系统长期行为的转变。这类长暂态可能导致不同状态之间的 regime shift（ regime 转变），在较长时间段内呈现出与替代稳定态动力学相似的特征。在消费者-资源相互作用中，资源的群体防御是一种可能引发长暂态的动力学机制。此外，离散繁殖脉冲导致的种群时间滞后，无论是单独作用还是与群体防御引发的暂态共同作用，都有可能产生长暂态。本研究分析了一个消费者-资源系统模型中长暂态的发生可能性，该模型中的资源具备群体防御能力，且以离散繁殖脉冲的方式进行繁殖。我们通过对脉冲微分方程进行离散化，构建了这个离散时间模型。该系统在资源的灭绝状态和环境容纳量状态附近表现出 crawl-by（爬行式）暂态。此外，我们在系统中识别出一个 transcritical bifurcation（ transcritical 分岔），在该分岔下会出现 ghost limit cycle（幽灵极限环）。这些暂态会在较长的暂态时间段内表现得类似稳定态。我们利用微扰理论，基于这些暂态估算了系统的暂态持续时间。这项工作推进了人们对系统如何在不同状态间转变、在特定 regime 中停留的时长，以及哪些生态动力学可能导致长暂态的理解。
英文摘要：
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. We develop this discrete-time model by discretizing a pulse differential equation. This system exhibits crawl-by transients near the extinction and carrying capacity states of resource. In addition, we identify a transcritical bifurcation in our system, under which a ghost limit cycle appears. These transients resemble stable states for a prolonged transient time period. 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.
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