scholarly journals Stability Switches and Hopf Bifurcations in a Second-Order Complex Delay Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
M. Roales ◽  
F. Rodríguez
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Second Order ◽  
Delay Equation ◽  
Hopf Bifurcations ◽  
Order Complex ◽  
Stability Switches ◽  
Delay Differential ◽  
Complex Coefficients

The existence of stability switches and Hopf bifurcations for the second-order delay differential equation x′′t+ax′t-τ+bxt=0,  t>0, with complex coefficients, is studied in this paper.

scholarly journals Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-20
Author(s):  
Xiaoqian Cui ◽  
Junjie Wei
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Fourth Order ◽  
Delay Differential Equation ◽  
Center Manifold ◽  
Hopf Bifurcations ◽  
Stability Switches ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Delay Differential

A kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results.

scholarly journals Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
R. Rath ◽  
N. Misra ◽  
L. Padhy
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
T Tau

AbstractIn this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE) $$\left[ {r(t)(y(t) - p(t)y(t - \tau ))'} \right]^\prime + q(t)G(y(h(t))) = 0$$ are obtained, where q, h ∈ C([0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C ([0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ+. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.

Exponential stability of a second order delay differential equation without damping term

2015 ◽  
Vol 258 ◽  
pp. 483-488 ◽  
Author(s):  
Leonid Berezansky ◽  
Alexander Domoshnitsky ◽  
Mikhail Gitman ◽  
Valery Stolbov
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Second Order ◽  
Damping Term ◽  
Delay Differential

Nonoscillation and exponential stability of the second order delay differential equation with damping

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Leonid Berezansky ◽  
Alexander Domoshnitsky ◽  
Mikhail Gitman ◽  
Valery Stolbov
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Second Order ◽  
Delay Differential

AbstractFor a delay differential equation

scholarly journals Stability Switches in a First-Order Complex Neutral Delay Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. Roales ◽  
F. Rodríguez
Keyword(s):  
Delay Equation ◽  
Order Complex ◽  
Stability Switches ◽  
Neutral Delay ◽  
First Order ◽  
Complex Coefficients

Stability of the first-order neutral delay equationx′(t)+ax′(t−τ)=bx(t)+cx(t−τ)with complex coefficients is studied, by analyzing the existence of stability switches.

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