کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9501901 1338798 2005 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Global stability of periodic orbits of non-autonomous difference equations and population biology
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Global stability of periodic orbits of non-autonomous difference equations and population biology
چکیده انگلیسی
Elaydi and Yakubu showed that a globally asymptotically stable(GAS) periodic orbit in an autonomous difference equation must in fact be a fixed point whenever the phase space is connected. In this paper we extend this result to periodic nonautonomous difference equations via the concept of skew-product dynamical systems. We show that for a k-periodic difference equation, if a periodic orbit of period r is GAS, then r must be a divisor of k. In particular sub-harmonic, or long periodic, oscillations cannot occur. Moreover, if r divides k we construct a non-autonomous dynamical system having minimum period k and which has a GAS periodic orbit with minimum period r. Our methods are then applied to prove a conjecture by J. Cushing and S. Henson concerning a non-autonomous Beverton-Holt equation which arises in the study of the response of a population to a periodically fluctuating environmental force such as seasonal fluctuations in carrying capacity or demographic parameters like birth or death rates.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 208, Issue 1, 1 January 2005, Pages 258-273
نویسندگان
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