scholarly journals h-Stability for Differential Systems Relative to Initial Time Difference

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Peiguang Wang ◽  
Xiaowei Liu
Keyword(s):  
Differential System ◽  
Time Difference ◽  
Initial Time ◽  
Stability Criteria ◽  
Differential Systems ◽  
The Relationship

This paper investigates the relationship between an unperturbed differential system and a perturbed differential system that have initial time difference. Notions ofh-stability for differential systems with initial time difference are introduced, and stability criteria are formulated by using variation of parameter techniques.

scholarly journals Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Coşkun Yakar ◽  
Mustafa Bayram Gücen
Keyword(s):  
Differential System ◽  
Lyapunov Functions ◽  
Lyapunov Functional ◽  
Initial Position ◽  
Time Difference ◽  
Initial Time ◽  
Qualitative Behavior ◽  
Lyapunov Functionals ◽  
Comparison Result ◽  
Differential Systems

We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. We compare the classical notion of stability of the causal differential systems to the notion of initial time difference stability of causal differential systems and present a comparison result in terms of Lyapunov functions. We have utilized Lyapunov functions and Lyapunov functional in the study of stability theory of causal differential systems when establishing initial time difference stability of the perturbed causal differential system with respect to the unperturbed causal differential system.

scholarly journals On Transformation and Oscillation of Linear Differential System

1977 ◽  
Vol 29 (2) ◽  
pp. 392-399 ◽  
Author(s):  
Donald F. St. Mary
Keyword(s):  
Differential System ◽  
Comparison Theorem ◽  
Linear Case ◽  
Linear Differential System ◽  
Oscillation Theorem ◽  
Differential Systems ◽  
Order Linear ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
The Relationship

In this paper we study second order linear differential systems. We examine the relationship between oscillation of n-dimensional systems and certain associated n-dimensional systems, where m ≧ n. Several theorems are presented which unify and encompass in the linear case a number of results from the literature. In particular, we present a transformation which extends an oscillation theorem due to Allegretto and Erbe [1], and a comparison theorem due to Kreith [9], and explains some work of Howard [7].

scholarly journals Stability, Boundedness, and Lagrange Stability of Fractional Differential Equations with Initial Time Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Muhammed Çiçek ◽  
Coşkun Yakar ◽  
Bülent Oğur
Keyword(s):  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Time Difference ◽  
Initial Time ◽  
Differential Inequalities ◽  
Differential Systems ◽  
Lagrange Stability ◽  
Fractional Differential Systems ◽  
Comparison Results ◽  
Fractional Differential

Differential inequalities, comparison results, and sufficient conditions on initial time difference stability, boundedness, and Lagrange stability for fractional differential systems have been evaluated.

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

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