Delay-independent global convergence in time-varying monotone systems of delay differential equations satisfying a scalability condition

2014 ◽  
Author(s):  
Eoin Devane ◽  
Ioannis Lestas
Keyword(s):  
Global Convergence ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Varying ◽  
Monotone Systems ◽  
Delay Differential

Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses

2020 ◽  
Vol 70 (5) ◽  
pp. 1231-1248
Author(s):  
Danfeng Luo ◽  
Zhiguo Luo
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence Results ◽  
Time Varying ◽  
Ulam Stability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Gronwall’S Inequality ◽  
Fractional Differential ◽  
Delay Differential ◽  
Stability Results

AbstractIn this paper, we mainly consider the existence and Hyers-Ulam stability of solutions for a class of fractional differential equations involving time-varying delays and non-instantaneous impulses. By the Krasnoselskii’s fixed point theorem, we present the new constructive existence results for the addressed equation. In addition, we deduce that the equations have Hyers-Ulam stable solutions by utilizing generalized Grönwall’s inequality. Some results in this literature are new and improve some early conclusions.

scholarly journals Stability Analysis Method for Periodic Delay Differential Equations with Multiple Distributed and Time-Varying Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Gang Jin ◽  
Xinyu Zhang ◽  
Kaifei Zhang ◽  
Hua Li ◽  
Zhanjie Li ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Milling Process ◽  
Spindle Speed ◽  
Time Varying ◽  
Typical Application ◽  
Variable Helix ◽  
Periodic Delay ◽  
Delay Differential

Dynamic stability problems leading to delay differential equations (DDEs) are found in many different fields of science and engineering. In this paper, a method for stability analysis of periodic DDEs with multiple distributed and time-varying delays is proposed, based on the well-known semidiscretization method. In order to verify the correctness of the proposed method, two typical application examples, i.e., milling process with a variable helix cutter and milling process with variable spindle speed, which can be, respectively, described by DDEs with the multidistributed and time-varying delays are considered. Then, comparisons with prior methods for stability prediction are made to verify the accuracy and efficiency of the proposed approach. As far as the milling process is concerned, the proposed method supplies a generalized algorithm to analyze the stability of the single milling systems associated with variable pith cutter, variable helix cutter, or variable spindle speed; it also can be utilized to analyze the combined systems of the aforementioned cases.

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