Consider a simple predator–prey model

with parameters a = 1.2, b = 0.6, c = 0.8, and d = 0.3. Employ initial conditions of x(0) = 2 and y(0) = 1 and integrate numerically from t = 0 to 30. Compare the performance of explicit Euler and Runge–Kutta fourth-order method for a time step of Δt = 0.0625. Plot time trajectories as well as phase plane plots for each method.

dx dt dy | dt = ax - bxy = -cy + dxy