Quantum Prey-Predator Dynamics: A Gaussian Ensemble Analysis

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.

Automated summary

Quantum mechanics plays a crucial role in modeling competitive ecological systems and self-organizing structures. The dynamics of prey-predator competition in phase space can be described within the framework of Weyl-Wigner quantum mechanics, with quantum states convoluted by statistical gaussian ensembles. Quantum modifications on the equilibrium and stability of the prey-predator dynamics can be identified through the Wigner current fluxes obtained from an onset Hamiltonian background. Additionally, emergent topological quantum domains affect the stability properties of gaussian ensembles localized around the equilibrium point, leading to extinction and revival scenarios or perpetual coexistence of prey and predator agents.