scholarly journals Bifurcation Analysis of a Chemostat Model of Plasmid-Bearing and Plasmid-Free Competition with Pulsed Input

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhong Zhao ◽  
Baozhen Wang ◽  
Liuyong Pang ◽  
Ying Chen
Keyword(s):  
Periodic Solution ◽  
Bifurcation Analysis ◽  
Bifurcation Theory ◽  
Chemostat Model ◽  
Periodic Oscillations ◽  
Free Competition ◽  
The Stability ◽  
Invasion Threshold ◽  
Standard Techniques

A chemostat model of plasmid-bearing and plasmid-free competition with pulsed input is proposed. The invasion threshold of the plasmid-bearing and plasmid-free organisms is obtained according to the stability of the boundary periodic solution. By use of standard techniques of bifurcation theory, the periodic oscillations in substrate, plasmid-bearing, and plasmid-free organisms are shown when some conditions are satisfied. Our results can be applied to control bioreactor aimed at producing commercial producers through genetically altered organisms.

ANALYSIS OF A MODEL OF PLASMID-BEARING, PLASMID-FREE COMPETITION IN A PULSED CHEMOSTAT

2006 ◽  
Vol 09 (03) ◽  
pp. 263-276 ◽  
Author(s):  
XIANGYUN SHI ◽  
XINYU SONG ◽  
XUEYONG ZHOU
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Bifurcation Theory ◽  
Continuous System ◽  
Impulsive Effect ◽  
Chemostat Model ◽  
Free Competition ◽  
The Stability ◽  
Invasion Threshold ◽  
Standard Techniques

We introduce and study a chemostat model with plasmid-bearing, plasmid-free competition and impulsive effect. According to the stability analysis of the boundary periodic solution, we obtain the invasion threshold of the plasmid-free organism and plasmid-bearing organism. Furthermore, by using standard techniques of bifurcation theory, we prove the system has a positive τ-periodic solution, which shows that the impulsive effect destroys the equilibria of the unforced continuous system and initiates the periodic solution. Our results can be applied to control bioreactors aimed at producing commercial products through genetically altered organisms.

scholarly journals Competition between Plasmid-Bearing and Plasmid-Free Organisms in a Chemostat with Pulsed Input and Washout

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Sanling Yuan ◽  
Yu Zhao ◽  
Anfeng Xiao
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Bifurcation Theory ◽  
Periodic Oscillations ◽  
The Stability ◽  
Invasion Threshold ◽  
Standard Techniques

We consider a model of competition between plasmid-bearing and plasmid-free organisms in the chemostat with pulsed input and washout. We investigate the subsystem with nutrient and plasmid-free organism and study the stability of the boundary periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields the invasion threshold of the plasmid-bearing organism. By using the standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, plasmid-free, and plasmid-bearing organisms. Numerical simulations are carried out to illustrate our results.

BIFURCATION OF A MUTUALISTIC SYSTEM WITH VARIABLE COEFFICIENTS AND IMPULSIVE EFFECTS

2009 ◽  
Vol 02 (03) ◽  
pp. 363-375 ◽  
Author(s):  
YONGZHEN PEI ◽  
YONG YANG ◽  
CHANGGUO LI
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Bifurcation Theory ◽  
Positive Periodic Solution ◽  
Variable Coefficients ◽  
Impulsive Effects ◽  
The Stability ◽  
Invasion Threshold ◽  
Standard Techniques

In this paper, we introduce and study an impulsive mutualistic model with variable coefficients. By using Floquent theorem, the invasion threshold and the stability of the boundary periodic solution are obtained. Furthermore, by using standard techniques of bifurcation theory, the existent condition of the positive periodic solution is obtained. Finally, numerical simulations are carried out to confirm the main theorems.

DYNAMIC COMPLEXITIES OF A CHEMOSTAT MODEL WITH PULSED INPUT AND WASHOUT AT DIFFERENT TIMES

2008 ◽  
Vol 11 (01) ◽  
pp. 65-76
Author(s):  
SHUWEN ZHANG ◽  
DEJUN TAN ◽  
HONGSHENG GU
Keyword(s):  
Period Doubling ◽  
Impulsive System ◽  
Bifurcation Diagrams ◽  
Complex Dynamic ◽  
Chemostat Model ◽  
Predator Prey ◽  
Periodic Input ◽  
The Stability ◽  
Invasion Threshold ◽  
Fixed Times

In this paper, we consider a predator–prey chemostat model with ratio-dependent Monod type functional response and periodic input and washout at different fixed times. We obtain an exact periodic solution with substrate and prey. The stability analysis for this periodic solutions yields an invasion threshold for the period of pulses of the predator. When the impulsive period is more than the threshold, there are periodic oscillations in the substrate, prey, and predator. If the impulsive period further increases, the system undergoes a complex dynamic process. By analyzing bifurcation diagrams, we can see that the impulsive system shows two kinds of bifurcation, which are period-doubling and period-halving.

scholarly journals Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays

2020 ◽  
pp. 93-105
Author(s):  
Jane Ireri ◽  
Ganesh Pokhariyal ◽  
Stephene Moindi
Keyword(s):  
Periodic Solution ◽  
Fourier Series ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Nutrient Input ◽  
Chemostat Model ◽  
Bifurcation Theorem ◽  
Interior Equilibrium ◽  
Limiting Nutrient ◽  
Discrete Delays

In this paper we analyze a Chemostat model of two species competing for a single limiting nutrient input varied periodically using a Fourier series with discrete delays. To understand global aspects of the dynamics we use an extension of the Hopf bifurcation theorem, a method that rigorously establishes existence of a periodic solution. We show that the interior equilibrium point changes its stability and due to the delay parameter it undergoes a Hopf bifurcation.Numerical results shows that coexistence is possible when delays are introduced and Fourier series produces the required seasonal variations. We also show that for small delays periodic variations of nutrients has more influence on species density variations than the delay.

Competition between Two Microorganisms in a Crowley-Martin Type Chemostat with Pulsed Input and Washout

2013 ◽  
Vol 781-784 ◽  
pp. 610-614
Author(s):  
Qing Lai Dong
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Chemostat Model ◽  
Periodic Oscillations ◽  
The Stability

In this paper, we introduce and study a competition Chemostat model with Crowley-Martin type functional response and pulsed input and washout. The stability of the boundary periodic solutions is investigated. We get that above some threshold there are periodic oscillations in substrate and microorganisms, which implies the coexistence of two species.

Application of Bifurcation Theory to Voltage Stability in Power System

2013 ◽  
Vol 811 ◽  
pp. 643-646
Author(s):  
Xue Song Zhou ◽  
Mo Chen ◽  
You Jie Ma
Keyword(s):  
Power System ◽  
Bifurcation Analysis ◽  
Bifurcation Point ◽  
Bifurcation Theory ◽  
Voltage Stability ◽  
Formal Definition ◽  
Voltage Stabilization ◽  
Advantages And Disadvantages ◽  
Voltage Instability ◽  
Dynamic Bifurcation

In order to study on the problem of voltage stability of power system, this paper describes the static bifurcation analysis and the dynamic bifurcation analysis in voltage stabilization analysis of power system and its relationship with the voltage stability,discusses the voltage instability caused by two main bifurcation formal definition, the occurrence of the conditions and the calculation of the bifurcation point, and points out advantages and disadvantages of various algorithms. Finally the paper looks forward to further study of the bifurcation theory in terms of voltage stability.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

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