TY - JOUR
T1 - Global dynamics of one class of nonlinear nonautonomous systems with time-varying delays
AU - Berezansky, L.
AU - Idels, L.
AU - Troib, L.
N1 - Funding Information:
The first author’s research was supported in part by the Israeli Ministry of Absorption . The second author’s research was supported by a grant from VIU, Canada .
PY - 2011/12/1
Y1 - 2011/12/1
N2 - 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.
AB - 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.
KW - Causal (Volterra) operators
KW - Equilibria
KW - Global stability
KW - Hopfield-type neural network
KW - Nicholson-type delay differential systems
KW - Nonautonomous systems
KW - Permanence and population dynamics
UR - http://www.scopus.com/inward/record.url?scp=80052788638&partnerID=8YFLogxK
U2 - 10.1016/j.na.2011.08.004
DO - 10.1016/j.na.2011.08.004
M3 - Article
AN - SCOPUS:80052788638
SN - 0362-546X
VL - 74
SP - 7499
EP - 7512
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 18
ER -