Absolute Stability and Conditional Stability in General Delayed Differential Equations
Some recent results for analyzing the stability of equilibrium of delay differential equations are reviewed. Systems of one or two equations in general form are considered, and the criterions for absolute stability or conditional stability are given explicitly. The results show how the stability depends on both the instantaneous feedback and the delayed feedback.
Partially supported by NSF grant DMS-1022648 and Shanxi 100-talent program.
- 4.Erneux, T.: Applied Delay Differential Equations, vol. 3 of Surveys and Tutorials in the Applied Mathematical Sciences. Springer, New York (2009)Google Scholar
- 6.Hale, J.K., Verduyn Lunel, S.M.: Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences. Springer, New York (1993)Google Scholar
- 10.Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering. Academic Press, Boston, MA (1993)Google Scholar
- 14.Ruan, S.: Delay differential equations in single species dynamics. Delay Differential Equations and Applications, vol. 205 of NATO Sci. Ser. II Math. Phys. Chem., pp. 477–517. Springer, Dordrecht (2006)Google Scholar
- 17.Smith, H.: An Introduction to Delay Differential Equations with Applications to the Life Sciences, vol. 57 of Texts in Applied Mathematics. Springer, New York (2011)Google Scholar
- 20.Wu, J.: Theory and Applications of Partial Functional-Differential Equations, vol. 119 of Applied Mathematical Sciences. Springer, New York (1996)Google Scholar