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I want to find the conditions of stability of a fixed point. consider the function "f" iterates to obtain fixed point "a":

[itex] x_{n+1}= f(x_n)[/itex]

for this dynamic system, the fixed point "a" is stable if we have:

[itex] |f ^{\prime}(a)| < 1[/itex]

Currently I'm working on a bit different dynamic system that made me confused to determine the stability conditions for an arbitrary point, say "a". This dynamic system is:

[itex] x_{n+1}= x_n + \lambda \left( f(x_n, x_{n-1}) - f(x_{n-1}, x_{n-2})\right)[/itex].

this system is not only related to time "n", but also related to times "n-1" and "n-2".

Can anybody help me or give me clue to find the conditions?

suppose [itex] f(x_n)= c * x_n + d* x_{n-1}[/itex]

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# Stability of fixed point

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