Stability and bifurcation analysis of a generalized scalar delay differential equation

2016 ◽  
Vol 26 (8) ◽  
pp. 084306 ◽  
Author(s):  
Sachin Bhalekar
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Bifurcation Analysis ◽  
Stability And Bifurcation ◽  
Stability And Bifurcation Analysis ◽  
Delay Differential

scholarly journals Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Xinchao Yang ◽  
Xiju Zong ◽  
Xingong Cheng ◽  
Zhenlai Han
Keyword(s):  
Differential Equation ◽  
Hepatitis B Virus ◽  
Virus Infection ◽  
Hepatitis B ◽  
Delay Differential Equation ◽  
Bifurcation Analysis ◽  
Hepatitis B Virus Infection ◽  
B Virus ◽  
Stability And Bifurcation Analysis ◽  
Delay Differential

The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. We show the existence of nonnegative equilibria under some appropriated conditions. The existence of the Hopf bifurcation with delayτat the endemic equilibria is established by analyzing the distribution of the characteristic values. The explicit formulae which determine the direction of the bifurcations, stability, and the other properties of the bifurcating periodic solutions are given by using the normal form theory and the center manifold theorem. Numerical simulation verifies the theoretical results.

A model of a fishery with fish stock involving delay equations

2009 ◽  
Vol 367 (1908) ◽  
pp. 4907-4922 ◽  
Author(s):  
P. Auger ◽  
Arnaud Ducrot
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Delay Differential Equation ◽  
Bifurcation Analysis ◽  
Infinite Delay ◽  
Steady States ◽  
Delay Equations ◽  
Fish Stock ◽  
Delay Differential

The aim of this paper is to provide a new mathematical model for a fishery by including a stock variable for the resource. This model takes the form of an infinite delay differential equation. It is mathematically studied and a bifurcation analysis of the steady states is fulfilled. Depending on the different parameters of the problem, we show that Hopf bifurcation may occur leading to oscillating behaviours of the system. The mathematical results are finally discussed.

On Complex Periodic Motions in a Time-Delayed, Double-Well Duffing Oscillator With Strong Excitation

2016 ◽  
Author(s):  
Albert C. J. Luo ◽  
Siyuan Xing
Keyword(s):  
Differential Equation ◽  
Bifurcation Analysis ◽  
Analytical Method ◽  
Particle Physics ◽  
Duffing Oscillator ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Stability And Bifurcation Analysis ◽  
Strong Excitation

The time-delayed double-well Duffing oscillator is extensively applied in engineering and particle physics. Determination of periodic motions in such a system is significant. Thus, in this paper, period-1 motions in the time-delayed double-well Duffing oscillator are discussed through a semi-analytical method. The semi-analytical method is based on the implicit mappings constructed by discretization of the corresponding differential equation. Complex period-1 motions are predicted and the corresponding stability and bifurcation analysis are completed. From predictions, complex periodic motions are simulated numerically, and the harmonic amplitudes and phases are presented. Through this study, the complexity of periodic motions in the time-delayed Duffing oscillator can be better understood.

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