1999/08/31 by Eldad Bettelheim, Oded Agam, Nadav M. Shnerb · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Discretization #Dynamics (music) #Fixed point #Limit (mathematics) #Limit cycle #Non-equilibrium thermodynamics #Opinion Dynamics and Social Influence #Phase (matter) #Quantum #cond-mat #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/s1386-9477(00)00268-x
published as Physica E 9, 600 (2001) · 9 pages, 3 figures included
arxiv created 2000/03/01 · openalex publication_date 2001/03/01 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
Diffusion limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed-point. This fixed-point becomes unstable due to discretization effects, a scenario similar to quantum phase transitions. As a result, the long-time asymptotic behavior of the system changes and the dynamics flows into a limit cycle. The results are verified by numerical simulations.