Dynamical Behavior Analysis of Fixed Points of Investment Competition Model

2011 ◽  
pp. 125-132
Author(s):  
Shujuan Guo ◽  
Bing Han ◽  
Chunmei Yuan
Keyword(s):  
Fixed Points ◽  
Behavior Analysis ◽  
Dynamical Behavior ◽  
Competition Model ◽  
Investment Competition

scholarly journals Finding the fixed points of a Boolean network from a positive feedback vertex set

2020 ◽  
Author(s):  
Julio Aracena ◽  
Luis Cabrera-Crot ◽  
Lilian Salinas
Keyword(s):  
Fixed Points ◽  
Positive Feedback ◽  
Boolean Network ◽  
Dynamical Behavior ◽  
Boolean Networks ◽  
Supplementary Information ◽  
Feedback Vertex Set ◽  
Executable File ◽  
Vertex Set ◽  
Regulatory Functions

Abstract Motivation In the modeling of biological systems by Boolean networks, a key problem is finding the set of fixed points of a given network. Some constructed algorithms consider certain structural properties of the regulatory graph like those proposed by Akutsu et al. and Zhang et al., which consider a feedback vertex set of the graph. However, these methods do not take into account the type of action (activation and inhibition) between its components. Results In this article, we propose a new algorithm for finding the set of fixed points of a Boolean network, based on a positive feedback vertex set P of its regulatory graph and which works, by applying a sequential update schedule, in time O(2|P|·n2+k), where n is the number of components and the regulatory functions of the network can be evaluated in time O(nk), k≥0. The theoretical foundation of this algorithm is due a nice characterization, that we give, of the dynamical behavior of the Boolean networks without positive cycles and with a fixed point. Availability and implementation An executable file of FixedPoint algorithm made in Java and some examples of input files are available at: www.inf.udec.cl/˜lilian/FPCollector/. Supplementary information Supplementary material is available at Bioinformatics online.

scholarly journals DYNAMICAL BEHAVIOR OF INTERACTING DARK ENERGY IN LOOP QUANTUM COSMOLOGY

2010 ◽  
Vol 25 (26) ◽  
pp. 4993-5007 ◽  
Author(s):  
KUI XIAO ◽  
JIAN-YANG ZHU
Keyword(s):  
Dark Energy ◽  
Fixed Points ◽  
Quantum Cosmology ◽  
Dynamical Behavior ◽  
Friedmann Equation ◽  
Loop Quantum Cosmology ◽  
Dynamical Equations ◽  
Interacting Dark Energy ◽  
Dynamical Behaviors ◽  
The Difference

The dynamical behaviors of interacting dark energy in loop quantum cosmology are discussed in this paper. Based on three defined dimensionless variables, we simplify the equations of the fixed points. The fixed points for interacting dark energy can be determined by the Friedmann equation coupled with the dynamical equations in Einstein cosmology. But in loop quantum cosmology, besides the Friedmann equation, the conversation equation also gives a constrain on the fixed points. The difference of stability properties for the fixed points in loop quantum cosmology and the ones in Einstein cosmology are also discussed.

scholarly journals Development of mandelbrot set for the logistic map with two parameters in the complex plane

2021 ◽  
Vol 6 (3 (114)) ◽  
pp. 47-56
Author(s):  
Wasan Saad Ahmed ◽  
Saad Qasim Abbas ◽  
Muntadher Khamees ◽  
Mustafa Musa Jaber
Keyword(s):  
Fixed Points ◽  
Critical Point ◽  
Complex Plane ◽  
Dynamical Behavior ◽  
Logistic Map ◽  
Mandelbrot Set ◽  
Complex Numbers ◽  
Iteration Function ◽  
Two Parameters ◽  
Positive Integers

In this paper, the study of the dynamical behavior of logistic map has been disused with representing fractals graphics of map, the logistic map depends on two parameters and works in the complex plane, the map defined by f(z,α,β)=αz(1–z)β. where  and  are complex numbers, and β is a positive integers number, the visualization method used in this work to generate fractals of the map and to inspect the relation between the value of β and the shape of the map, this visualization analysis showed also that, as the value of β increasing, as the number of humps in the function also increasing, and it demonstrate that is true also for the function’s first iteration , f2(x0)=f(f(x0)) and the second iteration , f3(x0)=f(f2(x0)), beside that , the visualization technique showed that the number of humps in that fractal is less than the ones in the second iteration of the original function ,the study of the critical points and their properties of the logistic map also discussed it, whereas finding the fixed point led to find the critical point of the function f, in addition , it haven proven for the set of all pointsα∈C and β∈N, the iteration function f(f(z) has an attractive fixed points, and belongs to the region specified by the disc |1–β(α–1)|<1. Also, The discussion of the Mandelbrot set of the function defined by the f(f(z)) examined in complex plans using the path principle, such that the path of the critical point z=z0 is restricted, finally, it has proven that the Mandelbrot set f(z,α,β) contains all the attractive fixed points and all the complex numbers  in which α≤(1/β+1) (1/β+1) and the region containing the attractive fixed points for f2(z,α,β) was identified

scholarly journals Dynamical Behavior of some families of cubic functions in complex plane

2019 ◽  
Vol 24 (7) ◽  
pp. 122
Author(s):  
Mizal H. Alobaidi ◽  
Omar Idan Kadham
Keyword(s):  
Fixed Points ◽  
Critical Point ◽  
Complex Plane ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Open Disc ◽  
Origin Point

The current study deals with the dynamical behavior of three cubic functions in the complex plane. Critical and fixed points of all of them were studied . Properties of every point were studied and the nature of them was determined if it is either attracting or repelling. First function  such that have two critical points  and three fixed points  such that is attracting when  is origin point As shown in figure (2).And  are attracting when  is the region specified by open disc  shown in figure (1.(c)).Second function  such that have two critical points   and three fixed points such that  is attracting when  and that its path is to the origin point as shown in figure (4).And  are attractive when  represents the open disc shown in the figure (3.(c)).Third function  such that  have one critical point  and three fixed points  is attracting that is path is the origin point and  are repelling as shown in figure (5). And all 2-cycles of  are repelling and unstable .   http://dx.doi.org/10.25130/tjps.24.2019.139

Nonlinear Behavior Analysis of a Rotor Supported on Fluid-Film Bearings

2005 ◽  
Vol 128 (1) ◽  
pp. 35-40 ◽  
Author(s):  
Guangyan Shen ◽  
Zhonghui Xiao ◽  
Wen Zhang ◽  
Tiesheng Zheng
Keyword(s):  
Behavior Analysis ◽  
Dynamical Behavior ◽  
Nonlinear Behavior ◽  
Fluid Film ◽  
Diagnostic Tools ◽  
Nonlinear Phenomena ◽  
Frequency Spectra ◽  
Nonlinear Dynamical ◽  
Synchronous Motion ◽  
Period Motion

A fast and accurate model to calculate the fluid-film forces of a fluid-film bearing with the Reynolds boundary condition is presented in the paper by using the free boundary theory and the variational method. The model is applied to the nonlinear dynamical behavior analysis of a rigid rotor in the elliptical bearing support. Both balanced and unbalanced rotors are taken into consideration. Numerical simulations show that the balanced rotor undergoes a supercritical Hopf bifurcation as the rotor spin speed increases. The investigation of the unbalanced rotor indicates that the motion can be a synchronous motion, subharmonic motion, quasi-period motion, or chaotic motion at different rotor spin speeds. These nonlinear phenomena are investigated in detail. Poincaré maps, bifurcation diagram and frequency spectra are utilized as diagnostic tools.

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