Periodic Solution of Linear Autonomous Dynamic System

2017 ◽  
pp. 98-105
Author(s):  
Serikbai A. Aisagaliev ◽  
Zhanat Kh. Zhunussova
Keyword(s):  
Periodic Solution ◽  
Dynamic System

HOMOCLINIC BIFURCATION IN SEMI-CONTINUOUS DYNAMIC SYSTEMS

2012 ◽  
Vol 05 (06) ◽  
pp. 1250059 ◽  
Author(s):  
CHUANJUN DAI ◽  
MIN ZHAO ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Vector Fields ◽  
Homoclinic Bifurcation ◽  
Homoclinic Bifurcations ◽  
Continuous Dynamic System ◽  
Continuous Dynamic ◽  
Theoretical Results

In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results.

The Necessary Condition for the Existence of the Periodic Solution of Honeycomb Sandwich Plate Dynamics Model

2014 ◽  
Vol 668-669 ◽  
pp. 281-284
Author(s):  
Ting Ting Quan ◽  
Jing Li ◽  
Xin Li ◽  
Shao Tao Zhu
Keyword(s):  
Periodic Solution ◽  
Dynamic System ◽  
Sandwich Plate ◽  
Curvilinear Coordinates ◽  
Necessary Condition ◽  
Unperturbed System ◽  
Closed Orbits ◽  
Honeycomb Sandwich ◽  
Honeycomb Sandwich Plate ◽  
Plate Dynamic

In this paper we investigate the necessary condition for the existence of the periodic solution of honeycomb sandwich plate dynamic system of two-degree-of-freedom. We establish the curvilinear coordinates frame on closed orbits of the unperturbed system of the honeycomb sandwich plate dynamic system and construct successor function. Then we get the necessary condition of the existence of periodic solution by judging the existence of the successor functions. The existence of periodic solutions is important for studying the stability of sandwich plates.

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.

ANALYSIS OF THE UNIVERSITY S VIABILITY AS COMPLEX DYNAMIC SYSTEM

2018 ◽  
Vol 27 (103) ◽  
pp. 264-272 ◽  
Author(s):  
V. P. Mygal, ◽  
◽  
G. V. Mygal
Keyword(s):  
Dynamic System ◽  
Complex Dynamic ◽  
Complex Dynamic System ◽  
The University
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