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class of second order differential equations , J. Differential Equations 82 (1989), 15-27. [5] CHANTURIJA, T. A.-KIGURADZE, I. T.: Asymptotic Properties of Nonautonomous Ordinary Differential Equations . Nauka, Moscow, 1990. (In Russian) [6] Dˇ ZURINA, J.: Asymptotic properties of the third order delay differential equations , Nonlinear Anal. 26 (1996), 33-39. [7] DˇZURINA, J.: Asymptotic properties of third-order differential equations with deviating argument , Czechoslovak Math. J. 44 (1994), 163-172. [8] Dˇ ZURINA, J.: Comparison Theorems for Functional

criteria for positive systems with time-varying delay: A delay decomposition technique, Circuits, Systems and Signal Processing 35(5): 1545-1561. Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, Wiley, New York, NY. Hale, J. and Lunel, S.M.V. (1993). Introduction to Functional Differential Equations, Springer, New York, NY. Hmamed, A., Rami, M.A., Benzaouia, A. and Tadeo, F. (2012). Stabilization under constrained states and controls of positive systems with time delays, Mechanical Systems and Signal Processing 18(2): 182-190. Junfeng

References [1] BELLEN, A.-ZENNARO, M.: Numerical Methods for Delay Differential Equations . Clarendon Press, Oxford, 2003. [2] ˇCERM´AK, J.: A change of variables in the asymptotic theory of differential equations with unbounded delays , J. Comput. Appl. Math. 143 (2002), 81-93. [3] ˇCERM´AK, J.: The asymptotics of solutions for a class of delay differential equations , Rocky Mountain J. Math. 33 (2003), 775-786. [4] ˇCERM´AK, J.: On the differential equation with power coefficients and proportional delays , Tatra Mt. Math. Publ. 38 (2007), 57-69. [5

References [1] ˇC ERM´AK, J.-KUNDR´AT, P.: Linear differential equations with unbounded delays and a forcing term, Abstr. Appl. Anal. 2004 (2004), 337-345. [2] ˇC ERM´AK, J.: On the differential equation with power coefficients and proportional de- lays, Tatra Mt. Math. Publ. 38 (2007), 57-69. [3] DERFEL, G.-VOGL, F.: On the asymptotics of solutions of a class of linear functional- -differential equations, European J. Appl. Math. 7 (1996), 511-518. [4] HEARD, M. L.: A change of variables for functional differential equations, J. Differential Equations 18 (1975

References Duda, J. (1986). Parametric Optimization Problem for Systems with Time Delay , Ph.D. thesis, AGH University of Science and Technology, Cracow. Duda, J. (1988). Parametric optimization of neutral linear system with respect to the general quadratic performance index, Archiwum Automatyki i Telemechaniki   33 (3): 448-456. Duda, J. (2010a). Lyapunov functional for a linear system with two delays, Control & Cybernetics   39 (3): 797-809. Duda, J. (2010b). Lyapunov functional for a linear system with two delays both retarded and neutral type, Archives of

References [1] DIBL´IK, J.-KOKSCH, N.: Positive solutions of the equation x ˙ ( t ) = −c ( t ) x ( t−τ ) in the critical case , J. Math. Appl. 250 (2000), 635-659. [2] DIBL´IK, J.-K´UDELˇC´IKOV´A, M.: Two classes of asymptotically different positive solutions of the equation y ˙( t ) = −f ( t, yt ), Nonlinear Anal. 70 (2009), 3702-3714. [3] DIBL´IK, J.-SVOBODA, Z.-ˇSMARDA, Z.: Explicit criteria for the existence of positive solutions for a scalar differential equation with variable delay in critical case , Comput. Math. Appl. 56 (2008), 556-564. [4

REFERENCES [1] AZBELEV, N. V.: About zeros of solutions of linear differential equations of the second order with delayed argument, Differ. Uravn. 7 (1971), 1147–1157. [2] AZBELEV, N. V.—MAKSIMOV, V. P.—RAKHMATULLINA, L. F.: Introduction to the Theory of Functional-Differential Equations . Nauka, Moscow, 1991. N. Azbelev, V. Maksimov, and L. Rakhmatulina, Introduction to the Theory of Functional Differential Equations, “Nauka”, Moscow, 1991, 280 pp. (in Russian). [3] DOMSHLAK, Y.: Comparison theorems of Sturm type for first and second order differential

1 Introduction We show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged systems of periodically forced systems of delay differential equations with constant delay. The well-known theory of averaging [ 14 , 15 , 16 , 17 , 18 , 19 , 20 ] studies the reduction, by means of time-dependent changes of variables, of (nonautonomous) forced systems of differential equations to autonomous time-independent systems (averaged systems). Such a reduction is useful because autonomous systems are easier

-time analysis of space geodetic observations, Journal of Geodesy, Vol. 83, No. 5, 397-401. Chen Q., Song S., Zhu W. (2012) An Analysis for Accuracy of Tropospheric Zenith Delay Calculated from ECMWF/NCEP Data over Asia, Chinese Journal of Geophysics, Vol. 55, No. 4, 275-283. Davis J., Herring T., Shapiro A., Rogers E., Elgered G. (1985) Geodesy by Radio Interferometry: Effects of Atmospheric Modelling Errors on Estimates of Baseline Lenght, Radio Science, Vol. 20, No. 6, 1593-1607. Herring T.A. (1992) Modelling atmospheric delays in the analysis of space geodetic data

. Another important factor that significantly affects the change of steady-state regimes of dynamical systems, is the presence of different in their physical substance, factors of delay. The factors of delay are always present in rather extended systems due to the limitations of signal transmission speed: stretching, waves of compression, bending, current strength, etc. In some cases, taking into account factors of delay leads only to minor quantitative changes in dynamical characteristics of pendulum systems. In other cases, taking into account these factors allow to