Chaos Simulation
[code]Investigation of deterministic chaos and bifurcation phenomena in a continuous tri-trophic food chain ($X, Y, Z$) governed by the Hastings-Powell ODE system with Holling type II functional responses:
$$\begin{cases} \dot{X} = X\left(1 - \dfrac{X}{K}\right) -
\dfrac{a_1 X Y}{1 + b_1 X} - h_X X \\[8pt] \dot{Y} = \dfrac{a_1
X Y}{1 + b_1 X} - \dfrac{a_2 Y Z}{1 + b_2 Y} - d_1 Y \\[8pt]
\dot{Z} = \dfrac{a_2 Y Z}{1 + b_2 Y} - d_2 Z \end{cases}$$
Hastings-Powell differential equations.
Analyzes strange attractors, Lyapunov exponents, bifurcation cascades under carrying capacity $K$, and chaos suppression via linear prey harvesting ($h_X$).