Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics.

Area of Science:

• Theoretical Physics
• Quantum Mechanics
• Mathematical Biology

Background:

• Investigates prey-predator systems using quantum mechanics.
• Focuses on topological quantum domains and quantum phase-space descriptions.
• Utilizes Weyl-Wigner quantum mechanics for analysis.

Purpose of the Study:

• To explore nonequilibrium and instability features in prey-predator-like systems.
• To map Lotka-Volterra (LV) dynamics onto a quantum framework.
• To quantify the influence of quantum fluctuations on system equilibrium and stability.

Main Methods:

• Employs the generalized Wigner flow for one-dimensional Hamiltonian systems.
• Maps LV equations to the Heisenberg-Weyl noncommutative algebra ([x,k]=i).
• Analyzes non-Liouvillian patterns using Wigner currents and Gaussian ensemble parameters.
• Considers discretized time to identify bifurcation regimes.

Main Results:

• Quantum distortions affect hyperbolic equilibrium and stability parameters of prey-predator dynamics.
• Nonstationarity and non-Liouvillianity are quantified via Wigner currents and Gaussian parameters.
• Discretized time reveals nonhyperbolic bifurcation regimes with chaotic patterns dependent on Gaussian localization.

Conclusions:

• Quantum fluctuations significantly influence the equilibrium and stability of Lotka-Volterra driven systems.
• The study extends the quantification of quantum effects from continuous (hyperbolic) to discrete (chaotic) domains.
• Demonstrates the applicability of the generalized Wigner information flow framework to complex systems.