scholarly journals Persistence and Stability for a Class of Forced Positive Nonlinear Delay-Differential Systems

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
D. Franco ◽  
C. Guiver ◽  
H. Logemann
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Breeding Programmes ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay ◽  
Stability Concept

AbstractPersistence and stability properties are considered for a class of forced positive nonlinear delay-differential systems which arise in mathematical ecology and other applied contexts. The inclusion of forcing incorporates the effects of control actions (such as harvesting or breeding programmes in an ecological setting), disturbances induced by seasonal or environmental variation, or migration. We provide necessary and sufficient conditions under which the states of these models are semi-globally persistent, uniformly with respect to the initial conditions and forcing terms. Under mild assumptions, the model under consideration naturally admits two steady states (equilibria) when unforced: the origin and a unique non-zero steady state. We present sufficient conditions for the non-zero steady state to be stable in a sense which is reminiscent of input-to-state stability, a stability notion for forced systems developed in control theory. In the absence of forcing, our input-to-sate stability concept is identical to semi-global exponential stability.

scholarly journals Second-Order Impulsive Delay Differential Systems: Necessary and Sufficient Conditions for Oscillatory or Asymptotic Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 722
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz ◽  
Ali Muhib ◽  
Shao-Wen Yao
Keyword(s):  
Asymptotic Behavior ◽  
Differential System ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Impulsive Delay ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient

In this work, we aimed to obtain sufficient and necessary conditions for the oscillatory or asymptotic behavior of an impulsive differential system. It is easy to notice that most works that study the oscillation are concerned only with sufficient conditions and without impulses, so our results extend and complement previous results in the literature. Further, we provide two examples to illustrate the main results.

Finite time stability of semilinear multi-delay differential systems

2017 ◽  
Vol 40 (9) ◽  
pp. 2948-2959
Author(s):  
JinRong Wang ◽  
Zijian Luo
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Differential Systems ◽  
Finite Time Stability ◽  
Alternative Approach ◽  
Representation Of Solutions ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Exponential Matrix

In this paper, we provide an alternative approach to study finite time stability for semilinear multi-delay differential systems with pairwise permutable matrices associated with the stand and generalized Landau symbol conditions for nonlinear terms. The explicit representation of solutions involving a special multi-delayed exponential matrix function is developed to establish sufficient conditions to guarantee the systems are finite time stable by virtue of Gronwall integral inequalities with delay. Finally, we demonstrate the validity of the designed method and discuss it using numerical examples.

scholarly journals Boundedness of Stochastic Delay Differential Systems with Impulsive Control and Impulsive Disturbance

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Liming Wang ◽  
Baoqing Yang ◽  
Xiaohua Ding ◽  
Kai-Ning Wu
Keyword(s):  
Stochastic Analysis ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Stochastic Delay ◽  
Analysis Techniques ◽  
Moment Boundedness ◽  
Delay Differential System ◽  
Delay Differential Systems ◽  
Delay Differential

This paper considers thep-moment boundedness of nonlinear impulsive stochastic delay differential systems (ISDDSs). Using the Lyapunov-Razumikhin method and stochastic analysis techniques, we obtain sufficient conditions which guarantee thep-moment boundedness of ISDDSs. Two cases are considered, one is that the stochastic delay differential system (SDDS) may not be bounded, and how an impulsive strategy should be taken to make the SDDS be bounded. The other is that the SDDS is bounded, and an impulsive disturbance appears in this SDDS, then what restrictions on the impulsive disturbance should be adopted to maintain the boundedness of the SDDS. Our results provide sufficient criteria for these two cases. At last, two examples are given to illustrate the correctness of our results.

Delay-independent Stability of Uncertain Control Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 277-283 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Mehdi Ahmadian
Keyword(s):  
Control Systems ◽  
Uncertain Systems ◽  
Extreme Values ◽  
Sufficient Conditions ◽  
Entire Family ◽  
Active Vibration ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Analytical Expressions

This paper will provide a study of the delay-independent stability of uncertain control systems, represented by a family of quasipolynomials with single time-delays. The uncertain systems that are considered here are delay differential systems whose parameters are known only by their lower and upper bounds. The results are given in the form of necessary and sufficient conditions along with the assumptions for the quasipolynomial families considered. The conditions are transformed into convenient forms, which provide analytical expressions that can be easily checked by commercially available computing tools. For uncertain systems represented by families of quasipolynomials, it is shown that the delay independent stability for the extreme values of parameters is not sufficient for the delay independent stability of the entire family. In addition, the family must satisfy some conditions for the interior values of each parameter within specially constructed frequency ranges. The implementation of the theorem that is suggested is demonstrated on an example system that includes a single degree of freedom system with an active vibration absorber, namely the Delayed Resonator.

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