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

L. Berezansky, L. Idels, L. Troib

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish
Pages (from-to)7499-7512
Number of pages14
JournalNonlinear Analysis, Theory, Methods and Applications
Volume74
Issue number18
DOIs
StatePublished - 1 Dec 2011

Keywords

  • Causal (Volterra) operators
  • Equilibria
  • Global stability
  • Hopfield-type neural network
  • Nicholson-type delay differential systems
  • Nonautonomous systems
  • Permanence and population dynamics

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