Nomadic-colonial switching with stochastic noise: subsidence-recovery cycles and long-term growth

In this paper, we analyze a population model comprising organisms that alternate between nomadic and colonial behaviours by considering stochastic noise. Incorporating stochastic noise into the population dynamics will allow a wide range of environmental fluctuations to be modelled. The theoretical framework is also generalized to include resource depletion by both nomadic and colonial sub-populations, and an ecologically realistic population size-dependent switching scheme is now proposed. We demonstrate the robustness of the present model to stochastic noise, and the use of novel generalized pure time-based switching schemes to achieve consecutive subsidence-recovery cycles and long-term proliferation. Our results are of relevance to many physical and biological systems.