scholarly journals Oscillatory Behavior of Nonlinear Delay Differential Equation

2018 ◽  
Vol 1000 ◽  
pp. 012037
Author(s):  
D Seethalakshmi ◽  
S Balamuralitharan
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Oscillatory Behavior ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

A Necessary and Sufficient Condition for the Oscillation of an Even Order Nonlinear Delay Differential Equation

1973 ◽  
Vol 25 (5) ◽  
pp. 1078-1089 ◽  
Author(s):  
Bhagat Singh
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Oscillatory Behavior ◽  
Necessary And Sufficient Condition ◽  
Even Order ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

In this paper we study the oscillatory behavior of the even order nonlinear delay differential equation(1)where(i) denotes the order of differentiation with respect to t. The delay terms τi σi are assumed to be real-valued, continuous, non-negative, non-decreasing and bounded by a common constant M on the half line (t0, + ∞ ) for some t0 ≧ 0.

Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation

2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Delay Differential Equation ◽  
Difference Method ◽  
Discrete System ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Nonstandard Finite Difference

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.

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