Stability, instability in delay equations modeling human respiration
نویسندگان
چکیده
منابع مشابه
Delay Dynamic Equations with Stability
The unification and extension of continuous calculus, discrete calculus, q-calculus, and indeed arbitrary real-number calculus to time-scale calculus, where a time scale is simply any nonempty closed set of real numbers, were first accomplished by Hilger in [4]. Since then, time-scale calculus has made steady inroads in explaining the interconnections that exist among the various calculuses, an...
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We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation x(t + 1) = a(t)x(t) + t−1 ∑ s=t−r b(t, s)x(s). Also, by displaying a slightly different Lyapunov functional we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is relaxing the condi...
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We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the delay difference equation x(t + 1) = a(t)x(t) + b(t)x(t− h). The highlight of the paper is the relaxing of the condition |a(t)| < 1. An instability criteria for the zero solution is obtained. Moreover, we will provide an example, in which we show that our theorems provide...
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Keywords: Delay dynamic equations Fixed point theory Lyapunov Periodic solutions Stability Time scales a b s t r a c t Let T be an arbitrary time scale that is unbounded above. By means of a variation of Lyapunov's method and contraction mapping principle this paper handles asymptotic stability of the zero solution of the completely delayed dynamic equations x ∆ (t) = −a(t)x(δ(t))δ ∆ (t). Moreo...
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منطقه ی آسیای مرکزی وقفقاز به عنوان منطقه ای تاریخی و به دلیل دارا بودن ذخایر عظیم هیدرو کربنی از اهمیت ویژه ای برخوردار است. کشورهای این منطقه از عوامل عمده ی بی ثباتی نظیر عوامل جغرافیایی، اقتصادی، امنیتی، اجتماعی و سیاسی رنج می برند. پس از فروپاشی اتحاد جماهیر شوروی کشورهای منطقه از نعمت استقلال ناخواسته ای برخوردار شدند که مشکلات فوق را برای آن ها چندین برابر می کرد. در این روند برخی از این...
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ژورنال
عنوان ژورنال: Journal of Mathematical Biology
سال: 1994
ISSN: 0303-6812,1432-1416
DOI: 10.1007/bf00573459