- Consider the following iterative map (a> 0, b> 0)
π₯π‘ = π₯π‘β1 + π β π ππ( π π₯π‘β1 )
Conduct linear stability analysis to determine whether this model is stable at its equilibrium point
π₯ππ = 0
- A two dimensional difference equation model is given
π₯π‘ = π₯π‘β1 + 2 π₯π‘β1 (1 β π₯π‘β1 ) β π₯π‘β1 π¦π‘β1
π¦π‘ = π¦π‘β1 + 2 π¦π‘β1 (1 β π¦π‘β1 ) β π₯π‘β1 π¦π‘β1
- Find all equilibrium points
- Calculate the Jacobian matrix at the equilibrium point where x > 0 and y > 0
- Calculate the Eigenvalues of the matrix obtained
Determine whether the equilibrium point is stable, unstable or Lyapunov stable
