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During recent years, the study of long transients has been expanded inecological theory to account for shifts in long-term behavior of ecologicalsystems. These long transients may lead to regime shifts between alternativestates that resemble the dynamics of alternative stable states for a prolongedperiod of time. One dynamic that potentially leads to long transients is thegroup defense of a resource in a consumer-resource interaction. Furthermore,time lags in the population caused by discrete reproductive pulses have thepotential to produce long transients, either independently or in conjunction tothe transients caused by the group defense. In this work, we analyze thepotential for long transients in a model for a consumer-resource system inwhich the resource exhibits group defense and reproduces in discretereproductive pulses. We develop this discrete-time model by discretizing apulse differential equation. This system exhibits crawl-by transients near theextinction and carrying capacity states of resource. In addition, we identify atranscritical bifurcation in our system, under which a ghost limit cycleappears. These transients resemble stable states for a prolonged transient timeperiod. We estimate the transient time of our system from these transientsusing perturbation theory. This work advances an understanding of how systemsshift between alternate states and their duration of staying in a given regimeand what ecological dynamics may lead to long transients.

Characterizing long transients in consumer-resource systems with group defense and nonreproductive stages