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On contraction of nonlinear difference equations with time‐varying delays
Author(s) -
Ngoc Pham Huu Anh,
Trinh Hieu,
Hieu Le Trung,
Huy Nguyen Dinh
Publication year - 2019
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.201700167
Subject(s) - mathematics , uniqueness , nonlinear system , contraction (grammar) , contraction mapping , exponential stability , invariant (physics) , contraction principle , mathematical analysis , exponential function , delay differential equation , simple (philosophy) , stability (learning theory) , control theory (sociology) , differential equation , fixed point , computer science , medicine , philosophy , physics , control (management) , epistemology , quantum mechanics , machine learning , artificial intelligence , mathematical physics
General nonlinear difference equations with time‐varying delays are considered. Explicit criteria for contraction of such equations are presented. Then some simple sufficient conditions for global exponential stability of equilibria and for stability of invariant sets are derived. Furthermore, explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are derived. Finally, the obtained results are applied to time‐varying discrete‐time neural networks with delay.