[SOLVED] COSC4320 Assignment 03

Description

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

𝑥_𝑡 = 𝑥_𝑡−1 + 2 𝑥_𝑡−1 (1 − 𝑥_𝑡−1 ) − 𝑥_𝑡−1 𝑦_𝑡−1

𝑦_𝑡 = 𝑦_𝑡−1 + 2 𝑦_𝑡−1 (1 − 𝑦_𝑡−1 ) − 𝑥_𝑡−1 𝑦_𝑡−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