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On exponential stability of nonlinear Volterra difference equations in phase spaces
Author(s) -
Ngoc Pham Huu Anh,
Hieu Le Trung
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400093
Subject(s) - mathematics , exponential stability , nonlinear system , exponential function , zero (linguistics) , stability (learning theory) , mathematical analysis , volterra equations , computer science , linguistics , philosophy , physics , quantum mechanics , machine learning
Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18 , 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks.