Bazykin's model

Let us consider the Bazykin's prey-predator model [Bazykin (1998), Kuznetsov (2004)]:

\begin{equation*} \begin{cases} \dot{x}_1 = x_1 - \dfrac{x_1 x_2}{1 + \alpha x_1} - \varepsilon x_1^2 \\ \dot{x}_2 = -\gamma x_2 + \dfrac{x_1 x_2}{1 + \alpha x_1} - \delta x_2^2 \end{cases}, \end{equation*}
with \(\gamma = 1\) and \(\varepsilon = 0.1\). You can visualize its phase portrait in the plane and on the Poincaré sphere: choose a value for \(\alpha\) and \(\delta\) (decimal numbers between \(0\) and \(1\)).


Simulation

\( \alpha = \)
\( \delta = \) You must enter decimal numbers between $0$ and $1$.

Phase portraits of the Bazykin's model


Bibliography

A.D. Bazykin. Nonlinear dynamics of interacting populations. World Scientific, 1998.

Y. Kuznetsov. Elements of Applied Bifurcation Theory. Applied Mathematical Sciences. Springer New York, 2004.