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Lotka-Volterra Model

Population Dynamics

Phase Space

System Parameters

System Analysis

Equilibrium Points:

  • Extinction: (0, 0)
  • Coexistence: (1.33, 10.00)

System Stability: stable oscillations

Understanding the Model

The Equations

dx/dt = αx - βxy

dy/dt = -γy + δxy

Where x is prey population and y is predator population

Parameters

  • α (alpha): Prey growth rate
  • β (beta): Predation rate
  • γ (gamma): Predator death rate
  • δ (delta): Predator growth efficiency

Key Behaviors

  • Populations naturally oscillate
  • Predator peaks lag behind prey peaks
  • System has two equilibrium points
  • Trajectories form closed orbits