Consider the discrete dynamical system \[ \left\{ \begin{array}{r c l} w_{ n +1} & = & 0.4 w_n \\ w_0 & = & -2.2.\\ \end{array} \right. \]
Calculate the equilibria analytically.
$E=$________
Compute the next three points of the solution.
$w_0=$________
$w_1=$________
$w_2=$________
$w_3=$________
On the graph below, label the equilibria and cobweb the dynamical system for four steps.
How does the graphical method compare with what you did analytically? Is the equilibrium stable or unstable?
Given the discrete dynamical system \[ \left\{ \begin{array}{r c l} x_{n+1} & = & 2x_n(1-x_n) \\ x_0 & = & \frac{1}{4}\\ \end{array} \right. \] calculate the equilibria analytically.
$x_0=$________
$x_1=$________
$x_2=$________
On the graph below, label the equilibria and cobweb the dynamical system for five steps.
How does the graphical method compare with what you did analytically? Can you determine if the equilibria are stable or unstable?
Given the discrete dynamical system \[ \left\{ \begin{array}{r c l} x_{n+1} & = & \frac{7}{2}x_n(1-x_n) \\ x_0 & = & \frac{1}{2}\\ \end{array} \right. \] calculate the equilibria analytically.
On the graph below, label the equilibria and cobweb the dynamical system for six steps.
Using cobwebbing determine if the equilibria are stable or unstable?