Agrawal, V., Zhang, C., Shapiro, A.D., Dhurjati, P.S.: A dynamic mathematical model to clarify signaling circuitry underlying programmed cell death control in arabidopsis disease resistance. Biotechnol. Prog. 20(2), 426–442 (2004)
Aguirregabiria, J.M., Etxebarria, J.R.: Fractal basin boundaries of a delay-differential equation. Phys. Lett. A 122(5), 241–244 (1987)
Balanov, A.G., Janson, N.B., Schöll, E.: Delayed feedback control of chaos: bifurcation analysis. Phys. Rev. E Stat. Nonlinear Soft. Matter. Phys. 71(1 Pt 2), 016222 (2005)
Bellen, A., Zennaro, M.: Numerical Methods for Delay Differential Equations. Oxford Univ. Press, Oxford (2003)
Bellman, R., Cooke, K.L.: Differential-Difference Equations. Rand Corporation, Santa Monica (1963)
Bernier, C., Manitius, A.: On semigroups in \(\mathbb{R}^n \times L^p\) corresponding to differential equations with delays. Can. J. Math. 30(5), 897–914 (1978)
Breda, D., Maset, S., Vermiglio, R.: Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB. Springer, New York (2015)
Briat, C.: Robust Stability Analysis in the \(\ast \)-Norm and Lyapunov–Razumikhin Functions for the Stability Analysis of Time-Delay Systems: (CDC-ECC 2011); Orlando, Florida, USA, 12–15 December 2011. IEEE, Piscataway, NJ (2011)
Briat, C.: Linear Parameter-Varying and Time-Delay Systems: Analysis, Observation, Filtering & Control. Springer, Berlin (2015)
Broer, H.W., Takens, F.: Dynamical Systems and Chaos. Springer, New York (2011)
Cao, Y.Y., Lin, Z., Hu, T.: Stability analysis of linear time-delay systems subject to input saturation. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 49(2), 233–240 (2002)
Chiang, H.D.: Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundation, BCU Methodologies, and Applications. Wiley, Hoboken (2011)
Chiang, H.D., Fekih-Ahmed, L.: Quasi-stability regions of nonlinear dynamical systems: theory. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 43(8), 627–635 (1996)
Chiang, H.D., Tada, Y.: Design and implementation of on-line dynamic security assessment. IEEJ Trans. Electr. Electron. Eng. 4(3), 313–321 (2009)
Coutinho, D.F., de Souza, C.E.: Delay-dependent robust stability and \(L^2\)-gain analysis of a class of nonlinear time-delay systems. Automatica 44(8), 2006–2018 (2008)
Curtain, R.F., Zwart, H.: An Introduction to Infinite-Dimensional Linear Systems Theory. Springer, New York (1995)
Dambrine, M.: Contribution à l’étude de la stabilité des systèmes à retards. Ph.D. thesis, Université Lille1-Sciences et Technologies (1994). http://ori.univ-lille1.fr/notice/view/univ-lille1-ori-127166
Daza, A., Wagemakers, A., Sanjuán, M.A.F.: Wada property in systems with delay. Commun. Nonlinear Sci. Numer. Simul. 43, 220–226 (2017)
Delfour, M., Mitter, S.: Hereditary differential systems with constant delays. I. General case. J. Differ. Equ. 12(2), 213–235 (1972)
de Souza, C.E., Coutinho, D.: Delay-dependent regional stabilization of nonlinear quadratic time-delay systems. IFAC Proc. Vol. 47(3), 10084–10089 (2014)
Diekmann, O., Verduyn Lunel, S.M., Gils, S.A., Walther, H.O.: Delay Equations: Functional-, Complex-, And Nonlinear Analysis. Springer, New York (1995)
Dombovari, Z., Iglesias, A., Molnar, T.G., Habib, G., Munoa, J., Kuske, R., Stépán, G.: Experimental observations on unsafe zones in milling processes. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 377(2153), 20180125 (2019)
Dombovari, Z., Wilson, R.E., Stepan, G.: Estimates of the bistable region in metal cutting. Proc. Math. Phys. Eng. Sci. 464(2100), 3255–3271 (2008)
Dudkowski, D., Jafari, S., Kapitaniak, T., Kuznetsov, N.V., Leonov, G.A., Prasad, A.: Hidden attractors in dynamical systems. Phys. Rep. 637, 1–50 (2016)
Efimov, D., Schiffer, J., Ortega, R.: Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids. Int. J. Control 89(5), 909–918 (2015)
Engelborghs, K., Luzyanina, T., Roose, D.: Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL. ACM Trans. Math. Softw. 28(1), 1–21 (2002)
Fridman, E.: Introduction to Time-Delay Systems: Analysis and Control. Springer, Cham (2014)
Fridman, E.: Tutorial on Lyapunov-based methods for time-delay systems. Eur. J. Control 20(6), 271–283 (2014)
Goldsztejn, A., Chabert, G.: Estimating the robust domain of attraction for non-smooth systems using an interval Lyapunov equation. Automatica 100, 371–377 (2019)
Gu, K., Kharitonov, V.L., Chen, J.: Stability of Time-Delay Systems. Birkhäuser, Boston (2003)
Haddock, J.R., Terjéki, J.: Liapunov-Razumikhin functions and an invariance principle for functional differential equations. J. Differ. Equ. 48(1), 95–122 (1983)
Hahn, W.: Stability of Motion. Springer, Berlin (1967)
Halanay, A.: Mathematics in Science and Engineering: Differential Equations: Stability, Oscillations, Time Lags. Elsevier, Amsterdam (1966)
Hale, J.K.: Sufficient conditions for stability and instability of autonomous functional-differential equations. J. Differ. Equ. 1(4), 452–482 (1965)
Hale, J.K., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer, New York (1993)
Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge (1981)
Hinrichsen, D., Pritchard, A.J.: Real and complex stability radii: a survey. In: Hinrichsen, D., Mårtensson, B. (eds.) Control of Uncertain Systems, Progress in Systems and Control Theory, pp. 119–162. Birkhäuser Boston, Boston (1990)
Hu, G., Davison, E.J.: Real stability radii of linear time-invariant time-delay systems. Syst. Control Lett. 50(3), 209–219 (2003)
Hunt, B.R., Sauer, T., Yorke, J.A.: Prevalence: a translation-invariant ’almost every’ on infinite-dimensional spaces. Bull. Am. Math. Soc. 27(2), 217–239 (1992)
Ilyashenko, Y.: Centennial history of Hilbert’s 16th problem. Bull. Am. Math. Soc. 39(03), 301–355 (2002)
Insperger, T., Ersal, T., Orosz, G. (eds.): Time Delay Systems: Theory, Numerics, Applications, and Experiments. Springer, Cham (2017)
Janssens, S.G.: On a normalization technique for codimension two bifurcations of equilibria of delay differential equations. Master thesis, Utrecht University, Utrecht (2010)
Jarlebring, E.: The spectrum of delay-differential equations: numerical methods, stability and perturbation. Dissertation, Technische Universität Carolo-Wilhelmina zu Braunschweig (2008)
Kazarinoff, N.D., Wan, Y.H., van den Driessche, P.: Hopf bifurcation and stability of periodic solutions of differential-difference and integro-differential equations. IMA J. Appl. Math. 21(4), 461–477 (1978)
Khalil, H.K.: Nonlinear Systems. Prentice Hall, Upper Saddle River (2002)
Kharitonov, V.L.: Time-Delay Systems: Lyapunov Functionals and Matrices. Birkhäuser Springer, New York (2013)
Kloeden, P.E., Rasmussen, M.: Nonautonomous Dynamical Systems. American Mathematical Society, Providence (2011)
Krasovskii, N.N.: The approximation of a problem of analytic design of controls in a system with time-lag. J. Appl. Math. Mech. 28(4), 876–885 (1964)
Krasovskii, N.N., Brenner, J.L.: Stability of Motion: Applications of Lyapunov’s Second Method to Differential Systems and Equations with Delay. Stanford University Press, Stanford (1963)
Kuznetsov, N.V., Leonov, G.A.: Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors. IFAC Proc. Vol. 47(3), 5445–5454 (2014)
Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer, New York (1998)
Lakshmanan, M., Senthilkumar, D.V.: Dynamics of Nonlinear Time-Delay Systems. Springer, Berlin (2010)
LaSalle, J.P., Artstein, Z.: The Stability of Dynamical Systems. Society for Industrial and Applied Mathematics, Philadelphia (1976)
Lee, E., Neftci, S., Olbrot, A.: Canonical forms for time delay systems. IEEE Trans. Autom. Control 27(1), 128–132 (1982)
Leng, S., Lin, W., Kurths, J.: Basin stability in delayed dynamics. Sci. Rep. 6, 21449 (2016)
Liu, K., Fridman, E.: Delay-dependent methods and the first delay interval. Syst. Control Lett. 64, 57–63 (2014)
Losson, J., Mackey, M.C., Longtin, A.: Solution multistability in first-order nonlinear differential delay equations. Chaos 3(2), 167–176 (1993)
Melchor-Aguilar, D., Niculescu, S.I.: Estimates of the attraction region for a class of nonlinear time-delay systems. IMA J. Math. Control Inf. 24(4), 523–550 (2006)
Menck, P.J., Heitzig, J., Marwan, N., Kurths, J.: How basin stability complements the linear-stability paradigm. Nat. Phys. 9(2), 89–92 (2013)
Michiels, W., Niculescu, S.I.: Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-based Approach. SIAM Soc. for Indust. and Appl. Math, Philadelphia (2014)
Minorsky, N.: Self-excited mechanical oscillations. J. Appl. Phys. 19(4), 332–338 (1948)
Molnar, T.G., Dombovari, Z., Insperger, T., Stépán, G.: On the analysis of the double hopf bifurcation in machining processes via centre manifold reduction. Proc. Math. Phys. Eng. Sci. 473(2207), 20170502 (2017)
Molnar, T.G., Dombovari, Z., Insperger, T., Stépán, G.: Bifurcation analysis of nonlinear time-periodic time-delay systems via semidiscretization. Int. J. Numer. Meth. Eng. 115(1), 57–74 (2018)
Niculescu, S.I.: Delay Effects on Stability: A Robust Control Approach. Springer, Berlin (2001)
Niculescu, S.I., Gu, K. (eds.): Advances in Time-Delay Systems. Springer, Berlin (2004)
Oliva, W.: Functional differential equations on compact manifolds and an approximation theorem. J. Differ. Equ. 5(3), 483–496 (1969)
Ott, W., Yorke, J.A.: Prevalence. Bull. Am. Math. Soc. 42(03), 263–291 (2005)
Otto, A., Just, W., Radons, G.: Nonlinear dynamics of delay systems: an overview. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 377(2153), 20180389 (2019)
Oxtoby, J.C.: Measure and Category: A Survey of the Analogies Between Topological and Measure Spaces. Springer, New York (1980)
Rantzer, A.: A dual to Lyapunov’s stability theorem. Syst. Control Lett. 42(3), 161–168 (2001)
Roose, D., Szalai, R.: Continuation and bifurcation analysis of delay differential equations. In: Krauskopf, B., Osinga, H.M., Galán-Vioque, J. (eds.) Numerical Continuation Methods for Dynamical Systems, pp. 359–399. Springer, Dordrecht (2007)
Schäfer, B., Matthiae, M., Timme, M., Witthaut, D.: Decentral smart grid control. New J. Phys. 17(5), 059502 (2015)
Scholl, T.H., Gröll, L.: Time delay in the swing equation: a variety of bifurcations. Chaos Interdiscip. J. Nonlinear Sci. 29(12), 123118 (2019)
Seuret, A., Gouaisbaut, F., Baudouin, L.: D1.1–Overview of Lyapunov methods for time-delay systems: Rapport laas no. 16308. HAL archives-ouvertes.fr (hal-01369516) (2016)
Shampine, L.F., Thompson, S.: Solving DDEs in matlab. Appl. Numer. Math. 37(4), 441–458 (2001)
Shang, H., Xu, J.: Delayed feedbacks to control the fractal erosion of safe basins in a parametrically excited system. Chaos Solitons Fractals 41(4), 1880–1896 (2009)
Sieber, J., Engelborghs, K., Luzyanina, T., Samaey, G., Roose, D.: DDE-BIFTOOL manual: Bifurcation analysis of delay differential equations. arXiv preprint (arXiv:1406.7144) (2014)
Smith, H.: An Introduction to Delay Differential Equations with Applications to the Life Sciences. Springer, New York (2011)
Sprott, J.C.: A simple chaotic delay differential equation. Phys. Lett. A 366(4–5), 397–402 (2007)
Stépán, G.: Chaotic motion of wheels. Veh. Syst. Dyn. 20(6), 341–351 (1991)
Sullivan, T.J.: Introduction to Uncertainty Quantification. Springer, Cham (2015)
Taylor, S.R., Campbell, S.A.: Approximating chaotic saddles for delay differential equations. Phys. Rev. E 75(4), 046215 (2007)
Villafuerte, R., Mondié, S.: On improving estimate of the region of attraction of a class of nonlinear time delay system. IFAC Proc. Vol. 40(23), 227–232 (2007)
Wu, M., He, Y., She, J.H.: Stability Analysis and Robust Control of Time-Delay Systems. Springer, Berlin (2010)
Yan, Y., Xu, J., Wiercigroch, M.: Estimation and improvement of cutting safety. Nonlinear Dyn. 53(2), 619 (2019)
Zaborszky, J., Huang, G., Zheng, B., Leung, T.C.: On the phase portrait of a class of large nonlinear dynamic systems such as the power system. IEEE Trans. Autom. Control 33(1), 4–15 (1988)