Critical slowing down along the separatrix of Lotka–Volterra model of competition

Sauvik Chatterjee () and Muktish Acharyya
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Sauvik Chatterjee: Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India
Muktish Acharyya: Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 09, 1-10

Abstract: The Lotka–Volterra model of competition has been studied by numerical simulations using the Runge–Kutta–Fehlberg algorithm. The stable fixed points, unstable fixed point, saddle node, basins of attraction, and the separatices are found. The transient behaviors associated with reaching the stable fixed point are studied systematically. It is observed that the time of reaching the stable fixed point in any one of the basins of attraction depends strongly on the initial distance from the separatrix. As the initial point approached the separatrix, this time was found to diverge logarithmically. The divergence of the time, required to reach the stable fixed point, indicates the critical slowing down near the critical point in equilibrium phase transition. A metastable behavior was also observed near the saddle fixed point before reaching the stable fixed point.

Keywords: Lotka–Volterra model of competition; principle of competitive exclusion; Runge–Kutta–Fehlberg algorithm; separatrix; relaxation time; critical slowing down; metastable lifetime (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123501188

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