The stability of inner collinear equilibrium points in the photogravitational elliptic restricted problem

1993 ◽  
Vol 199 (1) ◽  
pp. 139-146 ◽  
Author(s):  
V. V. Markellos ◽  
E. Perdios ◽  
K. Papadakis
Keyword(s):  
Restricted Problem ◽  
Equilibrium Points ◽  
Elliptic Restricted Problem ◽  
The Stability

scholarly journals Generalized Out-of-Plane Equilibrium Points in the Frame of Elliptic Restricted Three-Body Problem: Impact of Oblate Primary and Luminous-Triaxial Secondary

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Aminu Abubakar Hussain ◽  
Aishetu Umar
Keyword(s):  
Binary Systems ◽  
Equilibrium Points ◽  
Semimajor Axis ◽  
Three Body Problem ◽  
Out Of Plane ◽  
Elliptic Restricted Problem ◽  
The Stability ◽  
Zero Velocity Curves ◽  
Three Body ◽  
Plane Equilibrium

This paper studies the motion of a third body near the 1st family of the out-of-plane equilibrium points, L6,7, in the elliptic restricted problem of three bodies under an oblate primary and a radiating-triaxial secondary. It is seen that the pair of points (ξ0,0,±ζ0) which correspond to the positions of the 1st family of the out-of-plane equilibrium points, L6,7, are affected by the oblateness of the primary, radiation pressure and triaxiality of the secondary, semimajor axis, and eccentricity of the orbits of the principal bodies. But the point ±ζ0 is unaffected by the semimajor axis and eccentricity of the orbits of the principal bodies. The effects of the parameters involved in this problem are shown on the topologies of the zero-velocity curves for the binary systems PSR 1903+0327 and DP-Leonis. An investigation of the stability of the out-of-plane equilibrium points, L6,7 numerically, shows that they can be stable for 0.32≤μ≤0.5 and for very low eccentricity. L6,7 of PSR 1903+0327 and DP-Leonis are however linearly unstable.

scholarly journals A Catalogue of Periodic Orbits in the Elliptic Restricted 3-Body Problem

1992 ◽  
Vol 152 ◽  
pp. 171-174 ◽  
Author(s):  
R. Dvorak ◽  
J. Kribbel
Keyword(s):  
Periodic Orbits ◽  
Restricted Problem ◽  
Body Problem ◽  
Grid Size ◽  
Mass Ratios ◽  
Families Of Periodic Orbits ◽  
Elliptic Restricted Problem ◽  
The Stability

Results of families of periodic orbits in the elliptic restricted problem are shown for some specific resonances. They are calculated for all mass ratios 0 < μ < 1.0 of the primary bodies and for all values of the eccentricity of the orbit of the primaries e < 1.0. The grid size is of 0.01 for both parameters. The classification of the stability is undertaken according to the usual one and the results are compared with the extensive studies by Contopoulos (1986) in different galactical models.

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

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