Lotka-Volterra Phase Plane (2D) — Predator-Prey ODE Portrait

Prey-Predator Phase Plane

Classic Lotka-Volterra ODE pair, integrated with RK4 and plotted as a phase-plane orbit (prey vs predator) as well as population-vs-time curves.

Rate parameters

Prey growth rate a 1.00 Predation rate b 0.10 Predator efficiency c 0.075 Predator death rate d 0.50

Initial conditions

Initial prey P₀ 10 Initial predators Q₀ 5

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Equilibrium

Prey eq. P*

—

Pred eq. Q*

—

Cycle period

—

Max prey/pred

—

Equations

dP/dt = a·P − b·P·Q
dQ/dt = c·P·Q − d·Q
Integrated with 4th-order Runge-Kutta. The non-trivial equilibrium (P*,Q*) = (d/c, a/b) is a neutral centre — orbits are closed loops in the phase plane.

Prey: —
Predators: —
Period est.: —