Transitional Dynamics and Quasi-Periodic Solution Observed in Two Asymmetrical Coupled Oscillators

2009 ◽  
Vol E92-A (1) ◽  
pp. 270-278
Author(s):  
Kuniyasu SHIMIZU ◽  
Tetsuro ENDO ◽  
Takuya YOSHIMURA
Keyword(s):  
Periodic Solution ◽  
Coupled Oscillators ◽  
Transitional Dynamics

scholarly journals Stability of The Synchronization Manifold in An All-To-All Time LAG- Diffusively Coupled Oscillators

2009 ◽  
Vol 14 ◽  
pp. 45
Author(s):  
Adu A.M. Wasike
Keyword(s):  
Periodic Solution ◽  
Coupled Oscillators ◽  
Time Lag ◽  
Lattice System ◽  
Diffusive Coupling ◽  
The Stability ◽  
Synchronization Manifold

we consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. We use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. Each oscillator has a unique periodic solution that is attracting.     

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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