Switching Particle Systems for Foraging Ants and Phase Transitions in Path Selections

Ayana Ezoe (Department of Physics, Chuo University, Tokyo)

Joint work with M. Katori (Chuo) and H. Nishimori (Meiji)

​

Physica A 643 (2024) 129798.

1

27 August 2024

Random Media and Random Fields, Lorentz Center in Leiden

Outline

• Introductions
• Model
• Numerical Analysis
• Summary and Future Problems

2

3

Introductions

Switching of Cues by Foraging Ants

Foraging Ants

4

• Collective behavior and swarm intelligence have been studied.

​

​

• Ants reach food and come back to the nest by following pheromones dropped by other ants.

https://mas.kke.co.jp/

Edward O. Wilson and Bert Holldobler : `The Ants’, Belknap Press (1990), pp.265-279

Switching of Cues by Foraging Ants

Nishimori’s group experiments

5

Ogihara, Yamanaka, Akino, Izumi, Awazu, Nishimori : in `Mathematical Approaches to Biological Systems’, Springer (2015), pp.119-137

1. In a box, put a food source separated from the nest.

​

• The preliminarily extracted recruit pheromone was applied along the white line.

​

• Trajectories of ants in 10 minutes were recorded.

!

Ants perform not only

pheromone-mediated walks but also visual-cues-mediated walks.

Switching Particle Systems

6

Two-layer model (Switching interacting particle systems)

Floreani, Giardina, den Hollander, Nandan, Redig : J. Stat. Phys. 186 (2022) 33 (pp.45)

fast particles

7

Model

Stochastic Models for Foraging Path Selection

8

Two types of particles, two types of walks

Stochastic Models for Foraging Path Selection

9

Two types of particles, two types of walks

(When ants are moving from nest to food.)

Stochastic Models for Foraging Path Selection

10

Two types of particles, two types of walks

(When ants are moving from food to nest.)

Stochastic Models for Foraging Path Selection

11

Stochastic Models for Foraging Path Selection

12

Pheromone field (Time evolution)

Stochastic Models for Foraging Path Selection

13

Pheromone-mediated walks

Stochastic Models for Foraging Path Selection

14

Visual-cues-mediated walks

Extreme Cases

15

Slow particle Fast particle

16

Numerical Analysis

17

Definition of Nearly Optimal Paths

18

19

20

21

22

​

​

​

The size dependence seems to be small.

​

​

Data collapse in statistical mechanics.

23

1/L-plots

Continuous Phase Transitions

24

The critical values of order parameters.

Evaluation of Critical Exponents

25

Evaluation of Critical Exponents

26

Summary

27

• A new stochastic model on a lattice for the group behavior of foraging ants is proposed and numerically studied.

​

• A new application of switching interacting particle systems studied in probability theory is shown.

​

• Global changes observed in experiments in path selections of ants are realized as continuous phase transitions in the model.

​

• Order parameters are introduced to characterize path selections of ants and new types of phase transitions and critical phenomena are clarified.

Future Problems

28

We want to know the following.

​

​

• Mathematical description of interactions between ants through the pheromone field which the ants generated in the past.

​

​

• Mathematical theory for the phase transitions and critical phenomena in path selection for foraging ants.

29

Please see our paper;

arXiv:cond-mat.stat-mech/2311.01946,

Physica A 643 (2024) 129798.

​

Thank you very much for your attention!

Supplement (Scaling argument)

30

Supplement (Scaling argument)

31