2024/08/18 by Idan Sorin, Sorin, Idan, Michael Tulchinsky +1 · 1 citation
Mathematics · Physics and Astronomy · #Economics #FOS: Physical sciences #Geology #Mathematical Physics (math-ph) #Mathematical economics #Mathematics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2408.09525
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we are going to make an analytical and numerical analysis for the Thomas system. Physically, this system describes a particle, driving by a system of oscillators, dissipated by a dissipation term b > 0. Mathematically, this system is very interesting because it contains rich dynamics in it which is generated by only one bifurcation parameter b. Depending on the value of b, the system is undergo through a stable regime, limit cycles, infinite amount of bifurcations, a series growing to infinity of fixed points, and chaos containing multiple attractors. Another interesting behaviour of the system is in the limit of b goes to zero, which means that there is no dissipation term. The system is then containing an infinite number of fixed points and behaves like a Brownian motion.