A mathematical framework for collective foraging behavior of social insect colonies in multi-dynamic environments

Abstract

Understanding collective behavior is integral to disciplines including developmental biology, behavioral ecology, and sociology. In this investigation, we construct deterministic and stochastic models for exploring how internal factors (i.e., task demand) and external factors (i.e., dynamic environment) drive the collective foraging behavior of social insect colonies. Through theoretical analysis, we demonstrate the global stability of an interior equilibrium for the deterministic case, and study the existence of a unique stationary distribution for the stochastic case. Surprisingly, the global stability of the interior equilibrium and the existence of a unique stationary distribution of the proposed models do not depend on additional conditions. The main contribution of this work is to construct a new mathematical framework to explore the influence of internal stimulus and external fluctuation on the dynamics of social insect colonies, and to provide corresponding theoretical analysis methods.