Unbounded Solutions and Instability of Second Order DDE

2020 ◽  
pp. 269-295
Author(s):  
Leonid Berezansky ◽  
Alexander Domoshnitsky ◽  
Roman Koplatadze
Keyword(s):  
Second Order ◽  
Unbounded Solutions

scholarly journals Unbounded solutions of second order discrete BVPs on infinite intervals

2016 ◽  
Vol 09 (02) ◽  
pp. 357-369
Author(s):  
Hairong Lian ◽  
Jingwu Li ◽  
Ravi P. Agarwal
Keyword(s):  
Second Order ◽  
Unbounded Solutions ◽  
Infinite Intervals

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

2008 ◽  
Vol 18 (11) ◽  
pp. 3461-3471 ◽  
Author(s):  
A. P. MIJOLARO ◽  
L. F. C. ABERTO ◽  
N. G. BRETAS
Keyword(s):  
Asymptotic Behavior ◽  
Vector Field ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Second Order ◽  
Coupled Systems ◽  
Nonlinear Dynamical ◽  
Unbounded Solutions ◽  
Synchronization Region ◽  
Coupling Parameters

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

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