Permanence of an N-species cooperation system with time delays and feedback controls on time scales

Hong-tao, Zhang; Zhang, Fode

doi:10.1007/s12190-013-0734-5

Cited by 8 publications

(6 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So it is worthwhile considering the permanence of biological models. The permanence of biological systems has been discussed by many authors [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In the process of studying these problems, the comparison method plays a paramount role.…”

Section: Introductionmentioning

confidence: 99%

“…To the best of our knowledge, the permanence of ecosystem on time scales with feedback control was first investigated in [13]. The authors considered the -species cooperation system with time delays and feedback control…”

Section: Introductionmentioning

confidence: 99%

“…, ) are positive constants. = max{max 1≤ , ≤ , max 1≤ ≤ , max 1≤ ≤ } > 0, where T can be found in [13].…”

Section: Introductionmentioning

confidence: 99%

“…They first give the definition of the permanence of ecosystem (1), and the definition of the permanence of other ecosystems mentioned in this paper is similar. Definition 1 (see [13]). System (1) is said to be permanent if there exist -dimensional positive constant vectors * , * , * , and * , which are independent on the initial condition, such that, for any solution ( ( ), ( )…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Some Differential Inequalities on Time Scales and Their Applications to Feedback Control Systems

Fan

Wang

2017

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

This paper deals with feedback control systems on time scales. Firstly, we generalize the semicycle concept to time scales and then establish some differential inequalities on time scales. Secondly, as applications of these inequalities, we study the uniform ultimate boundedness of solutions of these systems. We give a new method to investigate the permanence of ecosystem on time scales. And some known results have been generalized. Finally, an example is given to support the result.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…, ) are positive constants. = max{max 1≤ , ≤ , max 1≤ ≤ , max 1≤ ≤ } > 0, where T can be found in [13].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some Differential Inequalities on Time Scales and Their Applications to Feedback Control Systems

Fan

Wang

2017

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

“…In recent years, a variety of dynamic equations on time scales have been investigated (see [1,2,3,4,5,6,11,12,17]). However, only few papers [7,15,16] published on the permanence for dynamic equation models on time scales, and up to now, there is no paper published on the permanence for impulsive dynamic equation models on time scales. Thus, it is worthwhile continuing to study the single-species system with impulsive effects on time scales.…”

Section: Introductionmentioning

confidence: 99%

Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales

Wang¹,

Li²

2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. Then we prove a Massera type theorem for impulsive dynamic equations on time scales and based on this theorem, we establish a criterion for the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results. Our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new.

show abstract

Dynamics for a hybrid non-autonomous prey–predator system with generalist predator and impulsive conditions on time scales

2022

View full text Add to dashboard Cite

In this paper, we investigate the dynamical behavior for a hybrid non-autonomous predator–prey system with Holling Type II functional response, impulsive effects and generalist predator on time scales, where our proposed model commutes between a continuous-time dynamical system and discrete-time dynamical system. By using comparison theorems, we first study the permanence results of the proposed model. Also, we established the uniformly asymptotic stability for the almost periodic solution of the proposed model. Finally, in the last section, we provide some examples with numerical simulation.

show abstract

Permanence of an N-species cooperation system with time delays and feedback controls on time scales

Cited by 8 publications

References 17 publications

Some Differential Inequalities on Time Scales and Their Applications to Feedback Control Systems

Some Differential Inequalities on Time Scales and Their Applications to Feedback Control Systems

Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales

Dynamics for a hybrid non-autonomous prey–predator system with generalist predator and impulsive conditions on time scales

Contact Info

Product

Resources

About