Periodically forced Pielou's equation

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Abstract

We investigate the global character of solutions of the periodically forced Pielou's equationxn+1=βnxn1+xn1,n=0,1,, and prove that when the sequence {βn} is periodic with prime period k, with positive values, and i=0k1βi>1, every positive solution converges to a periodic solution with prime period k.

Keywords

Boundedness
Convergence to periodic solution
Difference equation
Periodically forced equation
Pielou's equation

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