Exercise $1$

Consider the following $3$D dynamic system:

$x^{}=s(y-z)$

$y^{}=kx-yz$

$z^{}=x-z$

where $k$ and $s$ are parameters. Answer the following questions.

$.$

Identify the intervals where the steady states are hyperbolic. Set a value of $k$ in each

interval, simulate the system for different initial conditions and discuss the resulis

$($hint$.$ Initially choose i$.$c$.$ near the steady state and then explore other values