Global exponential stability for nonlinear delay differential systems
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We give a review on recent results for global stability for nonlinear functional differential equations. Such equations include delay differential equations, integro-differential equations and equations with distributed delay and are applied as mathematical models in Population Dynamics and other sciences. We also consider methods used to study global stability: constructing of Lyapunov functional, applications of special matrices such as M-matrix or special matrix functions such as matrix measure, method of matrix inequalities, which is very popular in papers on Control Theory, fixed point approach and using a notion of nonlinear Volterra operator.
Global stability, lyapunov functional, matrix measure, the method of matrix inequalities, the nonlinear volterra operator
Короткий адрес: https://sciup.org/147155183
IDR: 147155183 | DOI: 10.14529/ctcr170214
Список литературы Global exponential stability for nonlinear delay differential systems
- Gil M. Stability of Finite and Infinite Dimensional Systems, Kluwer Academic Publishers, 1998 DOI: 10.1007/978-1-4615-5575-9
- Idels L., Kipnis M. Stability Criteria for a Nonlinear Nonautonomous System with Delays. Appl. Math. Model., 2009, vol. 33, no. 5, pp. 2293-2297.
- Berezansky L., Idels L., Troib L. Global Dynamics of One Class of Nonlinear Nonautonomous Systems with Time-Varying Delays. Nonlinear Anal., 2011, vol. 74, no. 18, pp. 7499-7512.
- Gyӧri I., Hartung F., Turi J., Preservation of Stability in Delay Equations under Delay Perturbations, J. Math. Anal. Appl., 1998, vol. 220, pp. 290-312 DOI: 10.1006/jmaa.1997.5883
- So Joseph W.-H., Tang X.H., Zou Xingfu. Global Attractivity for Non-Autonomous Linear Delay Systems, Funkcial. Ekvac., 2004, vol. 47, no. 1, pp. 25-40.
- Berezansky L., Idels L., Troib L. Global Dynamics of Nicholson-Type Delay Systems with Applications. Nonlinear Anal. Real World Appl., 2011, vol. 12, no. 1, pp. 436-445.
- Berezansky L., Diblik J., Svoboda Z., Smarda Z. Simple Uniform Exponential Stability Conditions for a System of Linear Delay Differential Equations. Appl. Math. Comput., 2015, vol. 250, pp. 605-614 DOI: 10.1016/j.amc.2014.10.117
