استقرار الحلول الدورية للنظام غير الخطي المحايد للمعادلة الديناميكية ذات المتغيرات المتأخرة
DOI:
https://doi.org/10.37376/glj.vi67.5908الكلمات المفتاحية:
معادلة تكاملية، معادلة تفاضلية، غير خطي محايد، استقرار، دالة انكماشالملخص
يتم استخدام نظرية النقطة الثابتة في هذه الدراسة لتوفير نتائج الاستقرار للحل الصفري لنظام محايد غير خطي للمعادلات . التفاضلية التي تمتلك الدوال التفاضلية بدلالة الزمن
التنزيلات
المراجع
D. R. Smart. .1980. Fixed Point Theorems. Cambridge University Press.
H. Logemann and S. Townley. .1996. The effect of small delays in the feedback loop on the stability of neutral systems. Syst. Control Lett. Vol.27, No. 5. pp. 267–274.
H. Logemann and L. Pandol. .1994. A note on stability and stabilizability of neutral systems. IEEE Trans. Automat. Contr.. Vol.39. No.1. pp. 138–143.
J. Hale. .1980. Ordinary Differential Equations, Robert E. Krieger Publishing Company. New York . STABILITY FOR A NONLINEAR SYSTEM 261
J. K. Hale and S. M. Verduyn Lunel. .1993. Introduction to Functional Differential Equations. Springer Verlag.New York.
M. W. Spong. .1985. A theorem on neutral delay systems. Syst. Control Lett. Vol.6. No. 4 pp. 291–294.
R. K. Brayton. . 1966. Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutral type. Quart. Appl. Math. Vol.24, No.3, pp. 215–224.
V. P. Rubanik. .1969. Oscillations of Quasilinear Systems with Retardation. Nauka. Moscow.
Y. Kuang. .1993. Delay Differential Equations with Applications in Population Dynamics. San Diego: Academic Press.
T. A. Burton, L. Hatvani. .1989. Stability theorems for non-autonomous functional differential equations by Liapunov functionals. Tohoku Math. J. 41 295–306.
T. A. Burton. . 1985. Stability and Periodic Solutions of Ordinary and Functional Differential Equations. Academic Press. Orlando. Florida.
T. Yoshizawa. .1966.Stability Theory by Liapunov’s Second Method. Tokyo Math. Soc. Japan.
L. Hatvani. .1997. Annulus arguments in the stability theory for functional differential equations, Differential Integral Equations 10 (1) 975–1002.
Y. N. Raffoul. .2004. Stability in neutral nonlinear differential equations with functional delays using fixed-point theory. Math. Comp. Modelling 40 691–700.
T. A. Burton. .2006. Stability by Fixed Point Theory for Functional Differential Equations. Dover Publications. New York.
T. A. Burton. . 2003. Perron-type stability theorems for neutral equations. Nonlinear Anal. 55 285–297.
T. A. Burton. . 1998. A fixed point theorem of Krasnoselskii. Applied Mathematics Letters. 11 (1). 85–88. [18] A. A. Ben Fayed, H.A. Makhzoum, R.A. Elmansouri, A.K. Alshaikhly . .2021. Periodic solutions by Krasnoselskii fixed point theorem of neutral nonlinear system of dynamical equation with Variable Delays .International Journal of Scientific .Mathematical and Statistical Sciences .pp.27-32.
M. B. Mesmouli. A. Ardjouni. and A. Djoudi. .2016. Stability solution for a system of nonlinear neutral functional differential equations with functional delay. Dynamic Systems and Applications 25 253-262
C. Chicone. .1999. Ordinary differential equations with applications, Springer
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