Quantum prey-predator dynamics: a gaussian ensemble analysis

TL;DR

This paper explores quantum extensions of prey-predator ecological models using Gaussian ensemble analysis, revealing quantum effects on stability, equilibrium, and coexistence scenarios in microscopic systems.

Contribution

It introduces a quantum phase-space approach to prey-predator dynamics, analyzing how Gaussian ensembles influence stability and equilibrium in quantum ecological models.

Findings

Quantum distortions alter classical equilibrium points.

Emergent topological quantum domains affect stability.

Quantum parameters influence coexistence and extinction scenarios.

Abstract

Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey-predator competition dynamics in the framework of the Weyl-Wigner quantum mechanics. In this case, from the classical dynamics described by the Lotka-Volterra (LV) Hamiltonian, quantum states convoluted by statistical gaussian ensembles can be analytically evaluated. Quantum modifications on the patterns of equilibrium and stability of the prey-predator dynamics can then be identified. These include quantum distortions over the equilibrium point drivers of the LV dynamics which are quantified through the Wigner current fluxes obtained from an onset Hamiltonian background. In addition, for gaussian ensembles highly localized around the equilibrium point, stability properties are shown to be affected by emergent topological quantum domains which, in some cases, could lead either to extinction and revival scenarios or to the perpetual coexistence of both prey and predator agents identified as quantum observables in microscopic systems. Conclusively, quantum and gaussian statistical driving parameters are shown to affect the stability criteria and the time evolution pattern for such microbiological-like communities.