Browse Journals

[1] D. J. Acheson, A pendulum theorem, Proceedings of the Royal Society, Series A, London 443(1917) (1993), 239-245.

DOI: https://doi.org/10.1098/rspa.1993.0142

[2] D. J. Acheson and T. Mullin, Upside-down pendulums, Nature 366(6452) (1993), 215-216.

DOI: https://doi.org/10.1038/366215b0

[3] L. Berezansky, E. Braverman and L. Idels, Nicholson’s blowflies differential equations revisited: Main results and open problems, Applied Mathematical Modelling 34(6) (2010), 1405-1417.

DOI: https://doi.org/10.1016/j.apm.2009.08.027

[4] J. A. Blackburn, H. J. T. Smithand and N. Gronbech-Jensen, Stability and Hopf bifurcations in an inverted pendulum, American Journal of Physics 60(10) (1992), 903-908.

DOI: https://doi.org/10.1119/1.17011

[5] P. Borne, V. Kolmanovskii and L. Shaikhet, Steady-state solutions of nonlinear model of inverted pendulum, Theory of Stochastic Processes 5(3-4) (1999), 203-209.

[6] P. Borne, V. Kolmanovskii and L. Shaikhet, Stabilization of inverted pendulum by control with delay, Dynamic Systems and Applications 9(4) (2000), 501-515.

[7] N. Bradul and L. Shaikhet, Stability of the positive point of equilibrium of Nicholson’s blowflies equation with stochastic perturbations: Numerical analysis, Discrete Dynamics in Nature and Society (2007); Article ID 092959, pages 25.

DOI: https://doi.org/10.1155/2007/92959

[8] N. Bradul and L. Shaikhet, Stability of a difference analogue of the mathematic predator-prey model with stochastic perturbations, Mathematics and Mechanics, Odessa National University 14(20) (2009), 7-23 (in Russian).

[9] X. Ding and W. Li, Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay, Discrete Dynamics in Nature and Society (2006); Article ID 19413, 12 pages.

DOI: https://doi.org/10.1155/DDNS/2006/19413

[10] I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, Springer, Berlin, 1972.

[11] W. Gurney, S. Blythe and R. Nisbet, Nicholson’s blowflies revised, Nature 287 (1980), 17-21.

DOI: https://doi.org/10.1038/287017a0

[12] P. Imkeller and Ch. Lederer, Some formulas for Lyapunov exponents and rotation numbers in two dimensions and the stability of the harmonic oscillator and the inverted pendulum, Dynamic Systems 16(1) (2001), 29-61.

DOI: https://doi.org/10.1080/02681110010001289

[13] P. L. Kapitza, Dynamical stability of a pendulum when its point of suspension vibrates, Pergamon Press, Oxford 2 (1965), 714-725.

[14] V. L. Kocic and G. Ladas, Oscillation and global attractivity in a discrete model of Nicholson’s blowflies, Applicable Analysis 38(1-2) (1990), 21-31.

DOI: https://doi.org/10.1080/00036819008839952

[15] M. Levi, Stability of the inverted pendulum: A topological explanation, SIAM Review 30(4) (1988), 639-644.

[16] M. Levi and W. Weckesser, Stabilization of the inverted linearized pendulum by high frequency vibrations, SIAM Review 37(2) (1995), 219-223.

[17] C.-K. Lin, C.-T. Lin, Y. Lin and M. Mei, Exponential stability of nonmonotone traveling waves for Nicholson’s blowflies equation, SIAM Journal of Mathematical Analysis 46(2) (2014), 1053-1084.

DOI: https://doi.org/10.1137/12090439

[18] B. Liu, Global exponential stability of positive periodic solutions for a delayed Nicholson's blowflies model, Journal of Mathematical Analysis and Applications 412(1) (2014), 212-221.

DOI: https://doi.org/10.1016/j.jmaa.2013.10.049

[19] G. Maruyama, Continuous Markov processes and stochastic equations, Rendiconti del Circolo Matematico di Palermo: Series 2, 4(1) (1955), 48-90.

DOI: https://doi.org/10.1007/BF02846028

[20] G. J. Mata and E. Pestana, Effective Hamiltonian and dynamic stability of the inverted pendulum, European Journal of Physics 25(6) (2004), 717-721.

DOI: https://doi.org/10.1088/0143-0807/25/6/003

[21] R. Mitchell, Stability of the inverted pendulum subjected to almost periodic and stochastic base motion: An application of the method of averaging, International Journal of Non-Linear Mechanics 7(1) (1972), 101-123.

DOI: https://doi.org/10.1016/0020-7462(72)90025-X

[22] A. J. Nicholson, An outline of the dynamics of animal populations, Australian Journal of Zoology 2(1) (1954), 9-65.

DOI: https://doi.org/10.1071/ZO9540009

[23] A. I. Ovseyevich, The stability of an inverted pendulum when there are rapid random oscillations of the suspension point, Journal of Applied Mathematics and Mechanics 70(5) (2006), 762-768.

DOI: https://doi.org/10.1016/j.jappmathmech.2006.11.010

[24] L. Shaikhet, Stability of difference analogue of linear mathematical inverted pendulum, Discrete Dynamics in Nature and Society (2005); Article ID 149487, pp. 215-226.

DOI: https://doi.org/10.1155/DDNS.2005.215

[25] L. Shaikhet, About stability of a difference analogue of a nonlinear integro-differential equation of convolution type, Applied Mathematics Letters 19(11) (2006), 1216-1221.

DOI: https://doi.org/10.1016/j.aml.2006.01.004

[26] L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Difference Equations, Springer Science & Business Media, 2011.

DOI: https://doi.org/10.1007/978-0-85729-685-6

[27] L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, Springer Science & Business Media, 2013.

DOI: https://doi.org/10.1007/978-3-319-00101-2

[28] L. Shaikhet and J. Roberts, Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations, Advances in Difference Equations (2006); Article ID 073897, 22 pages.

DOI: https://doi.org/10.1155/ADE/2006/73897

[29] R. Sharp, Y.-H. Tsai and B. Engquist, Multiple time scale numerical methods for the inverted pendulum problem, In Book: Multiscale Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering, Berlin: Springer 44 (2005), 241-261.

DOI: https://doi.org/10.1007/3-540-26444-2_13

[30] JW-H. So and J. S. Yu, On the stability and uniform persistence of a discrete model of Nicholson’s blowflies, Journal of Mathematical Analysis and Applications 193(1) (1995), 233-244.

DOI: https://doi.org/10.1006/jmaa.1995.1231

[31] R. O. A. Taie and D. A. M. Bakhit, Some new results on the uniform asymptotic stability for Volterra integro-differential equations with delays, Mediterranean Journal of Mathematics 20 (2023); Article 280.

DOI: https://doi.org/10.1007/s00009-023-02489-w

[32] C. Tunc and O. Tunc, On the stability, integrability and boundedness analyses of systems of integro-differential equations with time-delay retardation, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Serie A: Matematicas 115(3) (2021); Article 115.

DOI: https://doi.org/10.1007/s13398-021-01058-8

[33] C. Tunc and O. Tunc, On the fundamental analyses of solutions to nonlinear integro-differential equations of the second order, Mathematics 10(22) (2022); Article 4235.

DOI: https://doi.org/10.3390/math10224235

[34] C. Tunc, O. Tunc and J. C. Yao, On the new qualitative results in integro-differential equations with Caputo fractional derivative and multiple kernels and delays, Journal of Nonlinear and Convex Analysis 23(11) (2022), 2577-2591

[35] C. Tunc, O. Tunc, C. F. Wen and J. C. Yao, On the qualitative analyses solutions of new mathematical models of integro-differential equations with infinite delay, Mathematical Methods in the Applied Sciences 46(13) (2023), 14087-14103.

DOI: https://doi.org/10.1002/mma.9306

[36] B. G. Zhang and H. X. Xu, A note on the global attractivity of a discrete model of Nicholson’s blowflies, Discrete Dynamics in Nature and Society 3 (1999); Article ID 362607, 51-55.

DOI: https://doi.org/10.1155/S1026022699000072