Bifurcations in the axial–torsional state-dependent delay model of rotary drilling

2018 ◽  
Vol 99 ◽  
pp. 13-30 ◽  
Author(s):  
Sunit K. Gupta ◽  
Pankaj Wahi
Keyword(s):  
Delay Model ◽  
Rotary Drilling ◽  
State Dependent ◽  
State Dependent Delay

Harvesting on a State-Dependent Time Delay Model

2020 ◽  
Vol 8 (1) ◽  
pp. 82-96
Author(s):  
Ruijun Xie ◽  
Xin Zhang ◽  
Wei Zhang
Keyword(s):  
Time Delay ◽  
Population Density ◽  
Positive Equilibrium ◽  
Delay Model ◽  
Stability Criteria ◽  
State Dependent ◽  
State Dependent Delay ◽  
Cooperation Model ◽  
Increasing Function ◽  
Positivity And Boundedness

AbstractIn this paper, we propose and analyze a cooperation model with harvesting and state-dependent delay, which is assumed to be an increasing function of the population density with lower and upper bound. The main purpose of this article is to obtain the dynamics of our model analytically by controlling the harvesting. We present results on positivity and boundedness of all populations. Criteria for the existence of all equilibria and uniqueness of a positive equilibrium are given by controlling the harvesting. Finally, the global exponentially asymptotical stability criteria of model is obtained by the improved Hanalay inequality.

State Dependent Regenerative Effect in Milling Processes

2011 ◽  
Vol 6 (4) ◽  
Author(s):  
Dániel Bachrathy ◽  
Gábor Stépán ◽  
János Turi
Keyword(s):  
Periodic Solutions ◽  
Large Amplitude ◽  
Chip Thickness ◽  
Hysteresis Phenomenon ◽  
Delay Model ◽  
Periodic Motions ◽  
Stability Calculation ◽  
State Dependent ◽  
Fold Bifurcation ◽  
State Dependent Delay

The governing equation of milling processes is generalized with the help of accurate chip thickness derivation resulting in a state dependent delay model. This model is valid for large amplitude machine tool vibrations and uses accurate nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool relative to the workpiece. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization around these periodic solutions by means of the semidiscretization method applied for the corresponding time-periodic delay system. Predictor-corrector method is developed to continue the periodic solutions as the bifurcation parameter, that is, the axial immersion is varied. It is observed that the influence of the state dependent delay on linear stability can be significant close to resonance where large amplitude forced vibrations occur. The existence of an unusual fold bifurcation is shown where a kind of hysteresis phenomenon appears between two different stable periodic motions.

Fold Bifurcation in the State-Dependent Delay Model of Milling: Analytical and Numerical Solutions

2011 ◽  
Author(s):  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Delay Differential Equation ◽  
Milling Process ◽  
The State ◽  
Delay Model ◽  
State Dependent ◽  
Fold Bifurcation ◽  
State Dependent Delay ◽  
Delay Differential

The standard models of the milling process describe the surface regeneration effect by a delay-differential equation with constant time delay. In this study, an improved two degree of freedom model is presented for milling process where the regenerative effect is described by an improved state dependent time delay model. The model contains exact nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool. This model is valid in case of large amplitude forced vibrations close to the near-resonant spindle speeds. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization of the state-dependent delay differential equation around these periodic solutions by means of the semi-discretization method. The results are validated by an advanced numerical time domain simulation where the chip thickness is calculated by means of Boolean algebra.

Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control

2014 ◽  
Vol 78 (3) ◽  
pp. 1891-1906 ◽  
Author(s):  
Xianbo Liu ◽  
Nicholas Vlajic ◽  
Xinhua Long ◽  
Guang Meng ◽  
Balakumar Balachandran
Keyword(s):  
Rotary Drilling ◽  
Stability And Control ◽  
State Dependent ◽  
State Dependent Delay ◽  
And Control

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

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