On asymptotic stability of a class of time–delay systems

References

• Bellman, R., & Cooke, K. L. (1963). Differential-difference equations. New York, NY: Academic Press.
   Google Scholar
• Cooke, K. L., & Grossman, Z. (1982). Discrete delay, distributed delay and stability switches. Journal of Mathematical Analysis Applications, 86, 592–627. doi:10.1016/0022-247X(82)90243-8
   Web of Science ®Google Scholar
• Cooke, K. L., & van den Driessche, P. (1986). On zeroes of some transcendental equations. Funkcialaj Ekvacioj, 29, 77–90. ( MR865215 (87m:34098))
   Google Scholar
• Elaydi, S. (2005). An introduction to difference equations (3rd ed.). New York, NY: Springer-Verlag.
   Google Scholar
• Freedman, H. I., & Kuang, Y. (1991). Stability switches in linear scalar neutral delay equation. Funkcialaj Ekvacioj, 34, 187–209.
   Google Scholar
• Gray, A., Greenhalgh, D., Hu, L., Mao, X., & Pan, J. A. (2011). Stochastic differential equation SIS epidemic model. SIAM Journal on Applied Mathematics, 71(3), 876–902. doi:10.1137/10081856X
   Web of Science ®Google Scholar
• Hrabalova, J. (2013). Stability properties of a discretized neutral delay differential equation. Tatra Mountains Mathematical Publications, 54, 83–92.
   Google Scholar
• Ikeda, N., & Watanabe, S. (2014). Stochastic differential equations and diffusion processes (Vol. 24). North Holland: Elsevier.
   Google Scholar
• Insperger, T., & Stépán, G. (2011). Semi-discretization for time-delay systems: Stability and engineering applications (Vol. 178). New York, Dordrecht, Heidelberg, London: Springer Science & Business Media.
   Google Scholar
• Khokhlovaa, T., Kipnis, M., & Malygina, V. (2011). The stability cone for a delay differential matrix equation. Applied Mathematics Letters, 24, 742–745. doi:10.1016/j.aml.2010.12.020
   Web of Science ®Google Scholar
• Kruthika, H. A., Mahindrakar, A. D., & Pasumarthy, R. (2017). Stability analysis of nonlinear time–delayed systems with application to biological models. International Journal of Applied Mathematics and Computer Science, 27(1), 91–103. doi:10.1515/amcs-2017-0007
   Web of Science ®Google Scholar
• Kuang, Y. (1993). Delay differential equations with applications in population dynamics. MR1218880 (94f:34001) Boston: Academic Press.
   Google Scholar
• Li, Y., Ma, W., Xiao, L., & Yang, W. (2017). Global stability analysis of the equilibrium of an improved time-delayed dynamic model to describe the development of T Cells in the thymus. Filomat, 31(2), 347–361. doi:10.2298/FIL1702347L
   Web of Science ®Google Scholar
• Liu, Q., Jiang, D., Shi, N., Hayat, T., & Alsaedi, A. (2016). Asymptotic behaviors of a stochastic delayed SIR epidemic model with nonlinear incidence. Communications in Nonlinear Science and Numerical Simulation, 40, 89–99. doi:10.1016/j.cnsns.2016.04.023
   Web of Science ®Google Scholar
• Matsunaga, H. (2008). Delay dependent and delay independent stability criteria for a delay differential system. American Mathematical Society, 42, 4305–4312. ( 136 Fields Inst. Commun.)
   Google Scholar
• Nakajima, H. (2014). On the stability of a linear retarded differential-difference equation. Funkcialaj Ekvacioj, 57, 43–56. doi:10.1619/fesi.57.43
   Web of Science ®Google Scholar
• Naresh, R., Tripathi, A., Tchuenche, J. M., & Sharma, D. (2009). Stability analysis of a time delayed SIR epidemic model with nonlinear incidence rate. Computers & Mathematics with Applications, 58(2), 348–359. doi:10.1016/j.camwa.2009.03.110
   Web of Science ®Google Scholar
• Ruan, S., & Wei, J. (2003). on the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamic of Continuous, Discrete and Impulsive Systems, 10, 863–874.
   Google Scholar
• Smith, H. (2010). An introduction to delay differential equations with applications to the life science. New York, NY: Springer.
   Google Scholar
• Stepan, G. (1989). Retarded dynamical systems: Stability and characteristic functions, pitman research notes in mathematics series (Vol. 210). New York, NY: Academic Press.
   Google Scholar
• Stepan, G. (1998). Delay-differential equation models for machine tool chatter. Dynamics and Chaos in Manufacturing Processes, 471152935, 165–192.
   Google Scholar
• Xu, R. (2012). Global stability of a delayed epidemic model with latent period and vaccination strategy. Applied Mathematical Modelling, 36(11), 5293–5300. doi:10.1016/j.apm.2011.12.037
   Web of Science ®Google Scholar