COSC 4320 Assignment 3 Solved

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

๐‘ฅ๐‘ก = ๐‘ฅ๐‘กโˆ’1 + ๐‘Ž โˆ— ๐‘ ๐‘–๐‘›( ๐‘ ๐‘ฅ๐‘กโˆ’1 )

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

๐‘ฅ๐‘’๐‘ž = 0

  1. A two dimensional difference equation model is given

๐‘ฅ๐‘ก = ๐‘ฅ๐‘กโˆ’1 + 2 ๐‘ฅ๐‘กโˆ’1 (1 โˆ’ ๐‘ฅ๐‘กโˆ’1 ) โˆ’ ๐‘ฅ๐‘กโˆ’1 ๐‘ฆ๐‘กโˆ’1

๐‘ฆ๐‘ก = ๐‘ฆ๐‘กโˆ’1 + 2 ๐‘ฆ๐‘กโˆ’1 (1 โˆ’ ๐‘ฆ๐‘กโˆ’1 ) โˆ’ ๐‘ฅ๐‘กโˆ’1 ๐‘ฆ๐‘กโˆ’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

Determine whether the equilibrium point is stable, unstable or Lyapunov stable

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