COSC4320-Assignment 3 Solved

1.     Consider the following iterative map (a 0, b 0)

 

𝑥𝑡 = 𝑥𝑡−1 + 𝑎 ∗ 𝑠𝑖𝑛( 𝑏 𝑥𝑡−1 )

 

Conduct linear stability analysis to determine whether this model is stable at its equilibrium point

𝑥𝑒𝑞 = 0

 

 

2.     A two dimensional difference equation model is given

 

𝑥𝑡 = 𝑥𝑡−1 + 2 𝑥𝑡−1 (1 − 𝑥𝑡−1 ) − 𝑥𝑡−1 𝑦𝑡−1  

 

𝑦𝑡 = 𝑦𝑡−1 + 2 𝑦𝑡−1 (1 − 𝑦𝑡−1 ) − 𝑥𝑡−1 𝑦𝑡−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