Trail formation based on directed pheromone deposition

Abstract

We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromone particles and interact with them through alignment interaction. The directed pheromone particles intend to model pieces of trails, while the alignment interaction translates the tendency for an ant to follow a trail when it meets it. Thanks to adequate quantitative descriptors of the trail patterns, the existence of a phase transition as the ant-pheromone interaction frequency is increased can be evidenced. We propose both kinetic and fluid descriptions of this model and analyze the capabilities of the fluid model to develop trail patterns. We observe that the development of patterns by fluid models require extra trail amplification mechanisms that are not needed at the Individual-Based Model level.

Self-organization of bacterial biofilms is facilitated by extracellular DNA

“…Common features displayed by these self-organized phenomena are the formation of trails that lead to the emergence of dramatic patterns of large-scale order (15). The processes leading to pattern formation in biological systems are likely to be more complex than the spontaneous emergence of patterns that are observed in nonliving systems and will involve an interplay of physical, chemical, and biological parameters (16,17).…”

Collective dynamics and self-organization: some challenges and an example

“…This section is an abridged version of [1] with some new numerical simulations. Our goal is to model the transition from a continuum medium towards a network pattern.…”

“…In [1], ants were initially located randomly with uniform spatial and orientation distributions. Simulations show that after an initial transient, a network of trails spontaneously emerges.…”

“…In [1], it is shown that the macroscopic model obtained in the limit ε → 0 is formally written as follows:…”

Application of Partial Differential Equations to Drum Head Vibration, Signal Transmission and Chemical Communication in Insects

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