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Existence And Stability Of Periodic Orbits Of Periodic Difference Equations With Delays, Ziyad Alsharawi, James Angelos, Saber Elaydi
Existence And Stability Of Periodic Orbits Of Periodic Difference Equations With Delays, Ziyad Alsharawi, James Angelos, Saber Elaydi
Mathematics Faculty Research
In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xn = ƒ(n−1, xn−k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p/gcd(p,k) - periodic difference equations. We give formulas for calculating the number of different periodic orbits under …