Lotka-Volterra variation without harvesting

Consider the system without prey harvesting, that is \begin{equation} \begin{split} x' &= x(a - cx -dy) \\ y' & = -y(b - ex) \end{split}\label{eq1} \end{equation} where all of $a, b, c, d, e$ are positive, and $a/c>b/e.$

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Simulation

The following simulation shows different solutions to the equations (\ref{eq1}) for different initial conditions and fixed values $d = 0.02$ and $e=0.02$.

Things to try:

• Drag the black point around. This point establishes the initial conditions.
• Change the parameters $a,b$ and $c$ to analyse the behaviour of the critical points $X_1$, $X_2$ and $X_3$.
• If needed, use the tools zoom in or out.

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