Moving averages for periodic delay differential and difference equations

2005 ◽  
pp. 158-183 ◽  
Author(s):  
B. Lehman ◽  
S. Weibel
Keyword(s):  
Difference Equations ◽  
Moving Averages ◽  
Periodic Delay ◽  
Delay Differential

scholarly journals Nonoscillation of Second-Order Dynamic Equations with Several Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-34 ◽  
Author(s):  
Elena Braverman ◽  
Başak Karpuz
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Comparison Theorems ◽  
Nonoscillatory Solutions ◽  
Several Delays ◽  
Delay Differential ◽  
Delay Difference Equations ◽  
Delay Difference

Existence of nonoscillatory solutions for the second-order dynamic equation(A0xΔ)Δ(t)+∑i∈[1,n]ℕAi(t)x(αi(t))=0fort∈[t0,∞)Tis investigated in this paper. The results involve nonoscillation criteria in terms of relevant dynamic and generalized characteristic inequalities, comparison theorems, and explicit nonoscillation and oscillation conditions. This allows to obtain most known nonoscillation results for second-order delay differential equations in the caseA0(t)≡1fort∈[t0,∞)Rand for second-order nondelay difference equations (αi(t)=t+1fort∈[t0,∞)N). Moreover, the general results imply new nonoscillation tests for delay differential equations with arbitraryA0and for second-order delay difference equations. Known nonoscillation results for quantum scales can also be deduced.

Oscillation and Global Attractivity in a Periodic Delay Equation

1996 ◽  
Vol 39 (3) ◽  
pp. 275-283 ◽  
Author(s):  
J. R. Graef ◽  
C. Qian ◽  
P. W. Spikes
Keyword(s):  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
All Solutions ◽  
Periodic Delay ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient

AbstractConsider the delay differential equationwhere α(t) and β(t) are positive, periodic, and continuous functions with period w > 0, and m is a nonnegative integer. We show that this equation has a positive periodic solution x*(t) with period w. We also establish a necessary and sufficient condition for every solution of the equation to oscillate about x*(t) and a sufficient condition for x*(t) to be a global attractor of all solutions of the equation.

scholarly journals General Solution of Linear Fractional Neutral Differential Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hai Zhang ◽  
Jinde Cao ◽  
Wei Jiang
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Difference Equations ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Linear Ordinary Differential Equations ◽  
Exponential Estimates ◽  
The Laplace Transform ◽  
Gronwall Integral Inequality ◽  
Delay Differential

This paper is concerned with the general solution of linear fractional neutral differential difference equations. The exponential estimates of the solution and the variation of constant formula for linear fractional neutral differential difference equations are derived by using the Gronwall integral inequality and the Laplace transform method, respectively. The obtained results extend the corresponding ones of integer order linear ordinary differential equations and delay differential equations.

scholarly journals A Method for Stability Analysis of Periodic Delay Differential Equations with Multiple Time-Periodic Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Gang Jin ◽  
Houjun Qi ◽  
Zhanjie Li ◽  
Jianxin Han ◽  
Hua Li
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Spindle Speed ◽  
Multiple Time ◽  
Variable Pitch ◽  
Periodic Delay ◽  
The Stability ◽  
Delay Differential ◽  
Time Periodic ◽  
Periodic Delays

Delay differential equations (DDEs) are widely utilized as the mathematical models in engineering fields. In this paper, a method is proposed to analyze the stability characteristics of periodic DDEs with multiple time-periodic delays. Stability charts are produced for two typical examples of time-periodic DDEs about milling chatter, including the variable-spindle speed milling system with one-time-periodic delay and variable pitch cutter milling system with multiple delays. The simulations show that the results gained by the proposed method are in close agreement with those existing in the past literature. This indicates the effectiveness of our method in terms of time-periodic DDEs with multiple time-periodic delays. Moreover, for milling processes, the proposed method further provides a generalized algorithm, which possesses a good capability to predict the stability lobes for milling operations with variable pitch cutter or variable-spindle speed.

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