scholarly journals Synchronization of delay-coupled nonlinear oscillators: An approach based on the stability analysis of synchronized equilibria

2009 ◽  
Vol 19 (3) ◽  
pp. 033110 ◽  
Author(s):  
Wim Michiels ◽  
Henk Nijmeijer
Keyword(s):  
Stability Analysis ◽  
Nonlinear Oscillators ◽  
Coupled Nonlinear Oscillators ◽  
The Stability

The Origin of Stability Indeterminacy in a Symmetric Hamiltonian

1984 ◽  
Vol 51 (2) ◽  
pp. 399-405 ◽  
Author(s):  
M. R. Hyams ◽  
L. A. Month
Keyword(s):  
Perturbation Theory ◽  
Stability Analysis ◽  
Hamiltonian System ◽  
Phase Plane ◽  
Nonlinear Oscillators ◽  
Two Dimensional ◽  
Periodic Motions ◽  
Coupled Nonlinear Oscillators ◽  
The Stability ◽  
Two Degree Of Freedom

The stability and bifurcation of periodic motions in a symmetric two-degree-of-freedom Hamiltonian system is studied by a reduction to a two-dimensional action-angle phase plane, via canonical perturbation theory. The results are used to explain why linear stability analysis will always be indeterminate for the in-phase mode in a class of coupled nonlinear oscillators.

NONLINEAR DYNAMICS OF DIGITAL PHASE-LOCKED LOOPS WITH DELAY

1994 ◽  
Vol 04 (03) ◽  
pp. 715-726 ◽  
Author(s):  
MARIA DE SOUSA VIEIRA ◽  
ALLAN J. LICHTENBERG ◽  
MICHAEL A. LIEBERMAN
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Behavior ◽  
Nonlinear Oscillators ◽  
Coupled Systems ◽  
Phase Locked Loops ◽  
Bifurcation Diagrams ◽  
Digital Phase ◽  
Coupled Nonlinear Oscillators ◽  
Digital Phase Locked Loops ◽  
The Stability

We investigate numerically and analytically the nonlinear dynamics of a system consisting of two self-synchronizing pulse-coupled nonlinear oscillators with delay. The particular system considered consists of connected digital phase-locked loops. We find mapping equations that govern the system and determine the synchronization properties. We study the bifurcation diagrams, which show regions of periodic, quasiperiodic and chaotic behavior, with unusual bifurcation diagrams, depending on the delay. We show that depending on the parameter that is varied, the delay will have a synchronizing or desynchronizing effect on the locked state. The stability of the system is studied by determining the Liapunov exponents, indicating marked differences compared to coupled systems without delay.

On the Stability Behavor of Bifurcated Normal Modes in Coupled Nonlinear Systems

1989 ◽  
Vol 56 (1) ◽  
pp. 155-161 ◽  
Author(s):  
C. H. Pak
Keyword(s):  
Nonlinear Systems ◽  
Calculus Of Variations ◽  
Normal Modes ◽  
Nonlinear Oscillators ◽  
Coupled Nonlinear Oscillators ◽  
Floquet’S Theory ◽  
Generic Bifurcation ◽  
The Stability ◽  
Floquet's Theory

The stability of bifurcated normal modes in coupled nonlinear oscillators is investigated, based on Synge’s stability in the kinematico-statical sense, utilizing the calculus of variations and Floquet’s theory. It is found, in general, that in a generic bifurcation, the stabilities of two bifurcated modes are opposite, and in a nongeneric bifurcation, the stability of continuing modes is opposite to that of the existing mode, and the stabilities of the two bifurcated modes are equal but opposite to that of the continuing mode. Some examples are illustrated.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

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