Synchronized Rhythmic Activity of Ants with Distributed Rest Periods

Abstract

Synchronization is a prevalent phenomenon in biological systems, including social insects such as ants. Certain ant species exhibit remarkable synchronization of their activities within the nest. To elucidate the underlying mechanisms of this coordinated behavior, we propose an integro-differential equation model that captures the autocatalytic nature of ant activation. Active ants can stimulate inactive individuals, leading to a cascade of arousal. By incorporating a stochastic component to represent variability in rest periods, we explore the conditions necessary for synchronization. Our analysis reveals a critical threshold for fluctuations in rest duration. Exceeding this threshold disrupts synchronization, driving the system towards a stable equilibrium. These findings offer valuable insights into the factors governing ant activity synchronization and highlight the delicate balance between model parameters required to generate rhythmic patterns.

Keywords

• synchronization
• collective behavior
• functional equations
• fixed-point analysis