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Consider the system of difference equations n>=0: x 1 (n+1)=x 1 (n)+ax 2 (n) x 2 (n+1)=bx 1 (n) Derive two conditions regarding a and

Consider the system of difference equations n>=0:

x₁(n+1)=x₁(n)+ax₂(n) x₂(n+1)=bx₁(n)

Derive two conditions regarding a and b such that if either of them holds, then the system has periodic solutions. Determine for each condition the period of the associated periodic solutions.

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