ملخص
In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays x(n) = f(n - 1, x(n-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 certain conditions. In addition, when p and k are relatively prime integers, we introduce what we call the pk-Sharkovsky's ordering of the positive integers, and extend Sharkovsky's theorem to periodic difference equations with delays. Finally, we characterize global stability and show that the period of a globally asymptotically stable orbit must be divisible by p.
اللغة الأصلية | English |
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الصفحات (من إلى) | 203-217 |
عدد الصفحات | 15 |
دورية | International Journal of Bifurcation and Chaos |
مستوى الصوت | 18 |
رقم الإصدار | 1 |
المعرِّفات الرقمية للأشياء | |
حالة النشر | Published - يناير 2008 |
منشور خارجيًا | نعم |
ASJC Scopus subject areas
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