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DY: Fachverband Dynamik und Statistische Physik

DY 33: Poster: Nonlinear Dynamics, Pattern Formation and Networks

DY 33.4: Poster

Mittwoch, 20. März 2024, 15:00–18:00, Poster C

Kirman’s herding model with stochastic resetting — •Pece Trajanovski¹, Petar Jolakoski¹, Arnab Pal², Ljupco Kocarev^1,3, and Trifce Sandev^1,4 — ¹Macedonian Academy of Sciences and Arts, Skopje, Macedonia — ²Institute of Mathematical Sciences, Chennai, India — ³Ss. Cyril and Methodius University in Skopje, Macedonia — ⁴University of Potsdam, Germany

Kirman’s herding model with stochastic resetting extends the seminal Kirman*s ants model by incorporating stochastic resetting, which mimics sharp external influences on the system. The dynamics are characterized by two essential parameters b and a, the first representing the strength of agents influence to convert others, and other signifying the likelihood of spontaneous preference alteration by each agent. The resetting rate (r) introduces a pivotal interplay, yielding unexpected outcomes in the mean first passage time to a specific binary choice.

Our approach enhances Kirman’s model by introducing exogenous factors, resulting in a more realistic herding/recruiting model adaptable to diverse behavioral scenarios. The analysis provides a comprehensive understanding, including the derivation of the probability distribution function solution, the distribution for the stationary case, and the mean first passage time distribution using the backward master equation. This exploration contributes valuable insights into the nuanced dynamics of collective decision-making and population configurations within complex systems, enriching our understanding of the Kirman’s herding model.

Keywords: Stochasticity; Stochastic resetting; herding model; decision-making; Local and non-local interactions