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Predator–Prey with Discrete Delay — Full Time Series (Forward Euler)

Parameters

1.00
1.0
1.00
0.020
0.60
0.0

Initial conditions & numerics

0.10
0.10
0.0100
1200

Model (unscaled): dx/dt = r·x·(1 − x/K) − m·x·y, dy/dt = −s·y + Y·e−sτ·m·x(t−τ)·y(t−τ). Forward Euler; delay index d = round(τ/Δt). History for t ≤ 0: x = x₀, y = y₀.

If curves look numerically unstable, reduce Δt.

Time series

Prey x(t) Predator y(t)

Phase plane (x vs y)

Trajectory