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 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.

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.

ADAPTABILITY AND SENSITIVITY OF COMPLEX SYSTEMS

2013 ◽  
Vol 23 (09) ◽  
pp. 1350163 ◽  
Author(s):  
ZHI-CHENG YE ◽  
QING-DUAN FAN ◽  
QIN-BIN HE ◽  
ZENG-RONG LIU
Keyword(s):  
Dynamical Systems ◽  
Complex Systems ◽  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Stable Equilibrium Point ◽  
Complex Dynamical Systems ◽  
Scientific Communities ◽  
Mathematical Definitions

Recently, the study on the dynamical behavior of complex dynamical systems has become a focal subject in the field of complexity. In particular, the system's adaptability and sensitivity have attracted increasing attention from various scientific communities. In this paper, we focus on some properties of complexity to gain a better understanding of it. Two descriptive mathematical definitions of attractors' adaptability and sensitivity are introduced from the viewpoint of dynamical systems. Then, these new descriptions are applied to analyze the adaptability and sensitivity of stable equilibrium points. In addition, a method is introduced for improving both the adaptability and sensitivity of a system with a stable equilibrium point.

ON STABILITY OF DIFFERENCE EQUATIONS IN PARTIALLY ORDERED SPACES

2018 ◽  
pp. 386-394
Author(s):  
Tatyana Vladimirovna Zhukovskaya ◽  
Ilya Alekseevich Zabrodskiy ◽  
Marina Vasilevna Borzova
Keyword(s):  
Equilibrium Point ◽  
Difference Equations ◽  
Stable Equilibrium ◽  
Stable Equilibrium Point ◽  
Partially Ordered ◽  
The Stability ◽  
Partially Ordered Spaces

We consider implicit difference equations in partially ordered spaces. We define the notion of a stable equilibrium point. The conditions of the stability is obtained. The study is based on the theory of partially ordered mappings.

scholarly journals Local Stability Analysis of a Mathematical Model of the Interaction of Two Populations of Differential Equations (Host-Parasitoid)

2016 ◽  
Vol 5 (1) ◽  
pp. 9
Author(s):  
Dewi Anggreini
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Stable Equilibrium ◽  
Jacobian Matrix ◽  
Equilibrium Points ◽  
Real Life ◽  
Host Population ◽  
Matrix Analysis ◽  
The Stability ◽  
Two Populations

<p>Mathematical model has many benefits in life, especially the development of science and application to other fields. The mathematical model seeks to represent real-life problems formulated mathematically to get the right solution. This research is the application of mathematical models in the field of biology that examines the interaction of the two populations that host populations and parasitoid populations. This study differs from previous studies that examine the interaction of two more species that prey and predators where predators kill prey quickly. In this study the parasitoid population slowly killing the host population by living aboard and take food from the host population it occupies. In this study of differential equations are used to construct a mathematical model was particularly focused on the stability of the local mathematical model of interaction of two differential equations that host and parasitoid populations. Stability discussed in this study are stable equilibrium points are obtained from the characteristic equation systems of differential equations host and parasitoid interactions. Type the stability of the equilibrium point is determined on the eigenvalues of the Jacobian matrix. Analysis of stability is obtained by determining the eigenvalues of the Jacobian matrix around equilibrium points. Having obtained the stable equilibrium points are then given in the form of charts and portraits simulation phase to determine the behavior of the system in the future.</p>

Dynamics of a Bistable Current-Controlled Locally-Active Memristor

2021 ◽  
Vol 31 (06) ◽  
pp. 2130018
Author(s):  
Meiyuan Gu ◽  
Guangyi Wang ◽  
Jingbiao Liu ◽  
Yan Liang ◽  
Yujiao Dong ◽  
...  
Keyword(s):  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Periodic Oscillation ◽  
Chaotic Oscillator ◽  
Stable Equilibrium Point ◽  
Storage Element ◽  
Active Devices ◽  
Oscillation Circuit

This paper presents a novel current-controlled locally-active memristor model to reveal the switching and oscillating characteristics of locally-active devices. It is shown that the memristor has two asymptotically stable equilibrium points on its power-off plot and therefore exhibits nonvolatility. Switching from one stable equilibrium point to another is achieved by applying a suitable current pulse. The locally-active characteristic of the memristor is measured by the DC [Formula: see text]–[Formula: see text] plot. A small-signal equivalent circuit on a locally-active operating point with the bias current [Formula: see text] is constructed for describing the characteristic of the locally-active region of the memristor. A periodic oscillator circuit composed of the locally-active memristor, a compensation inductor and a resistor is proposed, whose dynamics is analyzed in detail by using the Hopf bifurcation and the zeros and poles of the impendence function of the circuit. It is found that the locally-active memristor based circuit with different current biases or different initial conditions can exhibit different dynamics such as periodic oscillation and stable equilibrium point. If an energy storage element (capacitor) is added to the periodic oscillation circuit, a chaotic oscillator is obtained, which can exhibit abundant dynamics. The oscillation mechanism of the memristor-based oscillator is analyzed via dynamic route map (DRM), showing that the memristor is an essential device for generating periodic and chaotic oscillations, and its local activity is the cause for complex oscillations.

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 An Evolutionary Game Analysis of Internet Public Opinion Events at Universities: A Case from China

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hongying Wen ◽  
Kairong Liang ◽  
Yiquan Li
Keyword(s):  
Public Opinion ◽  
University Students ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Evolutionary Game ◽  
Stable Equilibrium Point ◽  
University Administration ◽  
Negative Effects ◽  
Internet Medium ◽  
The University

Internet public opinion events at universities in China occurred frequently, creating painful repercussions for reputation and stability of colleges and universities. To better cope with the problem, this paper explores an evolutionary mechanism of the university Internet public opinion events. Firstly, we discuss the interactions and behavior of three key participants: an Internet medium, university students as a whole, and administration. Secondly, we construct a tripartite evolutionary game model consisting of an Internet medium, student group, and university administration and then analyze and obtain the differential dynamic equations and equilibrium points. Subsequently, the evolutionary stable equilibrium is further analyzed. Finally, we employ numerical studies to examine how the tripartite behavior choices affect evolutionary paths and evolutionary equilibrium strategies. Results are derived as follows: under certain conditions, there exists an asymptotically stable equilibrium point for the tripartite evolutionary game. On the one hand, appropriate penalties and rewards should be provided to foster objectives and fair behaviors of the network medium. On the other hand, university students should be educated and guided to deal rationally with negative effects of Internet public opinion events. Moreover, online real-name authentication is an important and necessary measure. Finally, the university administration should release truthful, timely, and comprehensive information of Internet public opinion events to mitigate potential negative impacts.

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

scholarly journals Equilibrium Further Studied for Combined System of Cournot and Bertrand: A Differential Approach

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bingyuan Gao ◽  
Yueping Du
Keyword(s):  
General Equilibrium ◽  
Equilibrium Point ◽  
Price Competition ◽  
Dynamic Equilibrium ◽  
Equilibrium Points ◽  
Cournot Model ◽  
Combined System ◽  
Quantity Competition ◽  
Bertrand Model ◽  
The Stability

In general, quantity competition and price competition exist simultaneously in a dynamic economy system. Whether it is quantity competition or price competition, when there are more than three companies in one market, the equilibrium points will become chaotic and are very difficult to be derived. This paper considers generally dynamic equilibrium points of combination of the Bertrand model and Cournot model. We analyze general equilibrium points of the Bertrand model and Cournot model, respectively. A general equilibrium point of the combination of the Cournot model and Bertrand model is further investigated in two cases. The theory of spatial agglomeration and intermediate value theorem are introduced. In addition, the stability of equilibrium points is further illustrated on celestial bodies motion. The results show that at least a general equilibrium point exists in combination of Cournot and Bertrand. Numerical simulations are given to support the research results.

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