Angular velocity variations and stability of spatially explicit prey-predator systems.

Area of Science:

• Theoretical Ecology
• Dynamical Systems Theory
• Nonlinear Dynamics

Background:

• Lotka-Volterra models describe predator-prey dynamics.
• Understanding orbital instability is crucial for ecological and physical systems.
• Previous work has explored various stabilization mechanisms for oscillations.

Purpose of the Study:

• To analyze the linear instability of Lotka-Volterra orbits in a two-patch system.
• To identify the origin of instability in the absence of prey migration.
• To present an analogous model for coupled oscillators and integrate findings into a general framework.

Main Methods:

• Analysis of linear instability in the homogenous manifold of a two-patch Lotka-Volterra system.
• Investigation of the dependence of angular velocity on azimuthal angle.
• Development and analysis of a two coupled oscillator model.

Main Results:

• The study reveals that the linear instability originates from the dependence of angular velocity on the azimuthal angle.
• The system desynchronizes when exiting the slow part of its trajectory.
• An analogous two coupled oscillator model demonstrates the same type of linear instability.

Conclusions:

• The identified source of instability provides a new perspective on Lotka-Volterra dynamics.
• The findings facilitate the comparison and classification of oscillation stabilization mechanisms.
• This research contributes to a unified framework for understanding oscillatory systems.