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Global dynamics of one class of nonlinear nonautonomous systems with time-varying delays

Global dynamics of one class of nonlinear nonautonomous systems with time-varying delays

Authors :
Leonid Berezansky
Lev Idels
L. Troib
Source :
Nonlinear Analysis: Theory, Methods & Applications. 74:7499-7512
Publication Year :
2011
Publisher :
Elsevier BV, 2011.

Abstract

A class of nonautonomous systems of nonlinear delay differential equations was studied via construction of matrix inequalities and comparison techniques. The results for the nonautonomous systems with time-varying delays are novel, e.g., the global stability of differential equations with nonlinear (casual) Volterra operators is considered for the first time in the literature. Criteria obtained for permanence and global attractivity are explicit and hence are convenient for applying/verifying in practice. We illustrate applications of the results obtained to the nonautonomous and asymptotically autonomous Nicholson-type models.

Details

ISSN :
0362546X
Volume :
74
Database :
OpenAIRE
Journal :
Nonlinear Analysis: Theory, Methods & Applications
Accession number :
edsair.doi...........67e577c98d27a3438d92615aed36fb82
Full Text :
https://doi.org/10.1016/j.na.2011.08.004