Transient chaos and memory effect in the Rosenzweig-MacArthur system with dynamics of consumption rates

We consider the system of the Rosenzweig-MacArthur equations with one consumer and two resources. Recently, the model has been generalized by including an optimization of the consumption rates beta i [P. Gawronski et al., Chaos 32, 093121 (2022)]. Also, we have assumed that beta 1 + beta 2 = 1, which reflects the limited amount of time that can be devoted to a given type of resource. Here we investigate the transition to the phase where one of the resources becomes extinct. The goal is to show that the stability of the phase with two resources strongly depends on the initial value of beta i. Our second goal is to demonstrate signatures of transient chaos in the time evolution.