### 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.