scholarly journals Dynamics of transposable elements under the selection model

1999 ◽  
Vol 74 (2) ◽  
pp. 159-164 ◽  
Author(s):  
A. TSITRONE ◽  
S. CHARLES ◽  
C. BIÉMONT
Keyword(s):  
Equilibrium Point ◽  
Dynamic Characteristics ◽  
Time Scale ◽  
Copy Number ◽  
Stable Equilibrium ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Weak Selection ◽  
Strong Selection ◽  
Long Time

We examine an analytical model of selection against the deleterious effects of transposable element (TE) insertions in Drosophila, focusing attention on the asymptotic and dynamic characteristics. With strong selection the only asymptotically stable equilibrium point corresponds to extinction of the TEs. With very weak selection a stable and realistic equilibrium point can be obtained. The dynamics of the system is fast for strong selection and slow, on the human time scale, for weak selection. Hence weak selection acts as a force that contributes to the stabilization of mean TE copy number. The consequence is that under weak selection, and ‘out-of-equilibrium’ situation can be maintained for a long time in populations, with mean TE copy number appearing stabilized.

scholarly journals Addendum to ‘On an index policy for restless bandits'

1991 ◽  
Vol 23 (2) ◽  
pp. 429-430 ◽  
Author(s):  
Richard R. Weber ◽  
Gideon Weiss
Keyword(s):  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Index Policy ◽  
Fluid Approximation ◽  
Globally Asymptotically Stable ◽  
Restless Bandits

We show that the fluid approximation to Whittle's index policy for restless bandits has a globally asymptotically stable equilibrium point when the bandits move on just three states. It follows that in this case the index policy is asymptotic optimal.

scholarly journals Addendum to ‘On an index policy for restless bandits'

1991 ◽  
Vol 23 (02) ◽  
pp. 429-430 ◽  
Author(s):  
Richard R. Weber ◽  
Gideon Weiss
Keyword(s):  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Index Policy ◽  
Fluid Approximation ◽  
Globally Asymptotically Stable ◽  
Restless Bandits

We show that the fluid approximation to Whittle's index policy for restless bandits has a globally asymptotically stable equilibrium point when the bandits move on just three states. It follows that in this case the index policy is asymptotic optimal.

scholarly journals Research of Trajectory Optimization Approaches in Synthesized Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 336
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Trajectory Optimization ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Control Object ◽  
Symbolic Regression ◽  
Optimal Location ◽  
Stable Equilibrium Point ◽  
Stabilization System

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.

The Qualitative Analysis of Two Populations Commensalisms Model

2012 ◽  
Vol 524-527 ◽  
pp. 3705-3708
Author(s):  
Guang Cai Sun
Keyword(s):  
Qualitative Analysis ◽  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Mathematics Model ◽  
Stable Equilibrium Point ◽  
The Stability ◽  
Two Populations

This paper deals with the mathematics model of two populations Commensalisms symbiosis and the stability of all equilibrium points the system. It has given the conclusion that there is only one stable equilibrium point the system. This paper also elucidates the biology meaning of the model and its equilibrium points.

scholarly journals Author’s reply to: Comments on “Asymptotically stable equilibrium points in new chaotic systems”

Nova Scientia ◽  
2017 ◽  
Vol 9 (19) ◽  
pp. 906-909
Author(s):  
K. Casas-García ◽  
L. A. Quezada-Téllez ◽  
S. Carrillo-Moreno ◽  
J. J. Flores-Godoy ◽  
Guillermo Fernández-Anaya
Keyword(s):  
Dynamic Systems ◽  
Chaotic Systems ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Heteroclinic Orbits ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Linear Quadratic ◽  
The Monte Carlo Method

Since theorem 1 of (Elhadj and Sprott, 2012) is incorrect, some of the systems found in the article (Casas-García et al. 2016) may have homoclinic or heteroclinic orbits and may seem chaos in the Shilnikov sense. However, the fundamental contribution of our paper was to find ten simple, three-dimensional dynamic systems with non-linear quadratic terms that have an asymptotically stable equilibrium point and are chaotic, which was achieved. These were obtained using the Monte Carlo method applied specifically for the search of these systems.

Four-Wing Hidden Attractors with One Stable Equilibrium Point

2020 ◽  
Vol 30 (06) ◽  
pp. 2050086 ◽  
Author(s):  
Quanli Deng ◽  
Chunhua Wang ◽  
Linmao Yang
Keyword(s):  
Equilibrium Point ◽  
Chaotic Systems ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Stable Node ◽  
Stable Equilibrium Point ◽  
The Novel ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
Attraction Basin

Although multiwing hidden attractor chaotic systems have attracted a lot of interest, the currently reported multiwing hidden attractor chaotic systems are either with no equilibrium point or with an infinite number of equilibrium points. The multiwing hidden attractor chaotic systems with stable equilibrium points have not been reported. This paper reports a four-wing hidden attractor chaotic system, which has only one stable node-focus equilibrium point. The novel system can also generate a hidden attractor with one-wing and hidden attractors with quasi-periodic and periodic coexistence. In addition, a self-excited attractor with one-wing can be generated by adjusting the parameters of the novel system. The hidden attractors of the novel system are verified by the cross-section of attraction basins. And the hidden behavior is investigated by choosing different initial states. Moreover, the coexisting transient four-wing phenomenon of the self-excited one-wing attractor system is studied by the time domain waveforms and attraction basin. The dynamical characteristics of the novel system are studied by Lyapunov exponents spectrum, bifurcation diagram and Poincaré map. Furthermore, the novel hidden attractor system with four-wing and one-wing are implemented by electronic circuits. The hardware experiment results are consistent with the numerical simulations.

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