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23. 4. 2007.
Stability analysis of Pielou's equation with period-two coefficient
We study global attractivity of the period-two coefficient version of the delay logistic difference equation, also known as Pielou's equation, where We prove that for , zero is the unique equilibrium point. If , then zero is globally asymptotically stable, with basin of attraction given by the nonnegative quadrant of initial conditions. If , then zero is unstable, and a sequence converges to zero if and only if . If , then the sequence converges to the unique period-two solution where and are uniquely determined by the equations