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Lotka-Volterra

Feb 24, 2024 ODE Foundations 12 min read

Ordinary Differential Equations (15): Population Dynamics

Mathematical ecology from single-species to spatial: Malthus, logistic, Allee, Lotka-Volterra predator-prey and competition, age-structured Leslie matrices, metapopulations, and Fisher-KPP traveling waves.

Oct 28, 2023 ODE Foundations 8 min read

ODE Chapter 8: Nonlinear Systems and Phase Portraits

Step beyond linearity: predator-prey oscillations, competition exclusion, Van der Pol limit cycles, Hamiltonian systems, and the Poincare-Bendixson theorem -- the full toolkit for nonlinear 2D dynamics.