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Oscillation and stability in nonlinear delay differential equations of population dynamics

โœ Scribed by I. Kubiaczyk; S.H. Saker

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
453 KB
Volume
35
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

this paper, we shall study the oscillation of all positive solutions of the nonlinear delav differential eouation and x'(t) + ckvmx(t)xn(t -7)

x @+x"(t-7) = '

x'(t) + p(t) -F(t) r+xn(t-T) = 0 (**) about their equilibrium points. Also, we study the stability of these equilibrium points and prove that every nonoscillatory positive solution tends to the equilibrium point when t tends to infinity. Where equation (*) proposed by Mackey and Glass [l] for a "dynamic disease" involving respiratory disorders and equation (**) is one of the models proposed by Nazarenko [2] to study a control of a single population of cells.

๐Ÿ“œ SIMILAR VOLUMES

Oscillation of Nonlinear Delay Impulsive
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โœ Jurang Yan ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 97 KB

The oscillatory and asymptotic behavior of first-order nonlinear delay impulsive differential equations and inequalities is studied. Some new sharp sufficient conditions for oscillation and nonoscillation of solutions of the equations and inequalities are obtained. Many known results are improved. I

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The main result of this paper is to show oscillations of nonlinear impulsive delay differential equations are equivalent to those of corresponding linear impulsive delay differential equations. The results of this paper generalize some well-known results in the literature.