Aging by near-extinctions in many-variable interacting populations

Abstract

Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding, accompanied by a slowdown of the dynamics (aging). Here, we investigate the connection between near-extinction and aging by introducing an exactly solvable many-variable model, where the time derivative of each population size vanishes both at zero and some finite maximal size. We show that aging emerges generically when random interactions are taken between populations. Population sizes remain exponentially close (in time) to the absorbing values for extended periods of time, with rapid transitions between these two values. The mechanism for aging is different from the one at play in usual glassy systems: at long times, the system evolves in the vicinity of unstable fixed points rather than marginal ones.

References in corpus (8)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Phase space geometry and slow dynamics
• Marginally Stable Equilibria in Critical Ecosystems
• Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka-Volterra model of ecosystems
• Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise
• Glassy behaviour in disordered systems with non-relaxational dynamics
• Out-of-equilibrium dynamical mean-field equations for the perceptron model
• On the Dynamics of Liquids in the Large-Dimensional Limit

Cited by in corpus (8)

• Generalized Lotka-Volterra equations with random, non-reciprocal interactions: the typical number of equilibria
• Chaotic turnover of rare and abundant species in a strongly interacting model community
• Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions
• Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
• Dynamical Theory for Adaptive Systems
• Far-from-equilibrium complex landscapes
• Stabilization of macroscopic dynamics by fine-grained disorder in many-species ecosystems
• Critical behavior of a phase transition in the dynamics of interacting populations