1. Consider the following iterative map (a 0, b 0)
π₯π‘ = π₯π‘−1 + π ∗ π ππ( π π₯π‘−1 )
Conduct linear stability analysis to determine whether this model is stable at its equilibrium point
π₯ππ = 0
2. A two dimensional difference equation model is given
π₯π‘ = π₯π‘−1 + 2 π₯π‘−1 (1 − π₯π‘−1 ) − π₯π‘−1 π¦π‘−1
π¦π‘ = π¦π‘−1 + 2 π¦π‘−1 (1 − π¦π‘−1 ) − π₯π‘−1 π¦π‘−1
1. Find all equilibrium points
2. Calculate the Jacobian matrix at the equilibrium point where x 0 and y 0
3. Calculate the Eigenvalues of the matrix obtained
4. Determine whether the equilibrium point is stable, unstable or Lyapunov stable
