Skip to main content
Top
Published in: Journal of Applied Mathematics and Computing 1-2/2014

01-10-2014 | Original Research

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

Authors: Hongtao Zhang, Fode Zhang

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2014

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, an N-species cooperation system with time delays and feedback controls is proposed on time scales. In this process, some inequalities, which play a vital roles in the proof of main results, are firstly proved. Then, by applying the theory of differential inequality, sufficient conditions which guarantee the permanence of the system are obtained on time scales. Our results improve and complement some known results to some degree in the literature.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
2.
go back to reference Bohner, M., Peterson, A.: Dynamic Equations on Time Scales, an Introduction with Applications. Birkhäuser, Boston (2001) CrossRefMATH Bohner, M., Peterson, A.: Dynamic Equations on Time Scales, an Introduction with Applications. Birkhäuser, Boston (2001) CrossRefMATH
3.
go back to reference Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003) CrossRefMATH Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003) CrossRefMATH
4.
go back to reference Li, J.L., Shen, J.H.: Existence results for second-order impulsive boundary value problems on time scales. Nonlinear Anal. 70, 1648–1655 (2009) CrossRefMATHMathSciNet Li, J.L., Shen, J.H.: Existence results for second-order impulsive boundary value problems on time scales. Nonlinear Anal. 70, 1648–1655 (2009) CrossRefMATHMathSciNet
5.
go back to reference Hu, L.G.: Positive solutions to singular third-order three-point boundary value problems on time scales. Math. Comput. Model. 51, 606–615 (2010) CrossRefMATH Hu, L.G.: Positive solutions to singular third-order three-point boundary value problems on time scales. Math. Comput. Model. 51, 606–615 (2010) CrossRefMATH
6.
go back to reference Pang, Y.Y., Bai, Z.B.: Upper and lower solution method for a fourth-order four-point boundary value problems on time scales. Appl. Math. Comput. 215, 2243–2247 (2009) CrossRefMATHMathSciNet Pang, Y.Y., Bai, Z.B.: Upper and lower solution method for a fourth-order four-point boundary value problems on time scales. Appl. Math. Comput. 215, 2243–2247 (2009) CrossRefMATHMathSciNet
7.
go back to reference Chen, A.P., Dua, D.j.: Global exponential stability of delayed BAM network on time scale. Neurocomputing 71, 3582–3588 (2008) CrossRef Chen, A.P., Dua, D.j.: Global exponential stability of delayed BAM network on time scale. Neurocomputing 71, 3582–3588 (2008) CrossRef
8.
go back to reference Li, Y.K., Shu, J.Y.: Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Commun. Nonlinear Sci. Numer. Simul. 16, 3326–3336 (2011) CrossRefMATHMathSciNet Li, Y.K., Shu, J.Y.: Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Commun. Nonlinear Sci. Numer. Simul. 16, 3326–3336 (2011) CrossRefMATHMathSciNet
9.
go back to reference Zhang, Z.Q., Liu, K.Y.: Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales. Neural Netw. 24, 427–439 (2011) CrossRefMATH Zhang, Z.Q., Liu, K.Y.: Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales. Neural Netw. 24, 427–439 (2011) CrossRefMATH
10.
go back to reference Fan, M., Wang, K.: Global periodic solutions of a generalized n-species Gilpin-Ayala competition model. Comput. Math. Appl. 40, 1141–1151 (2000) CrossRefMATHMathSciNet Fan, M., Wang, K.: Global periodic solutions of a generalized n-species Gilpin-Ayala competition model. Comput. Math. Appl. 40, 1141–1151 (2000) CrossRefMATHMathSciNet
11.
go back to reference Chen, F.D.: Periodicity in a nonlinear predator-prey system with state dependent delays. Acta Math. Appl. Sin., Engl. Ser. 21, 49–60 (2005) CrossRefMATHMathSciNet Chen, F.D.: Periodicity in a nonlinear predator-prey system with state dependent delays. Acta Math. Appl. Sin., Engl. Ser. 21, 49–60 (2005) CrossRefMATHMathSciNet
12.
go back to reference Huo, H., Li, W.: Positive periodic solutions of a class of delay differential system with feedback control. Appl. Math. Comput. 148, 35–46 (2004) CrossRefMATHMathSciNet Huo, H., Li, W.: Positive periodic solutions of a class of delay differential system with feedback control. Appl. Math. Comput. 148, 35–46 (2004) CrossRefMATHMathSciNet
13.
go back to reference Chen, F.D., Liao, X.Y., Huang, Z.K.: The dynamic behavior of N-species cooperation system with continuous time delays and feedback controls. Appl. Math. Comput. 181, 803–815 (2006) CrossRefMATHMathSciNet Chen, F.D., Liao, X.Y., Huang, Z.K.: The dynamic behavior of N-species cooperation system with continuous time delays and feedback controls. Appl. Math. Comput. 181, 803–815 (2006) CrossRefMATHMathSciNet
14.
go back to reference Chen, L.J., Xie, X.D.: Permanence of an N-species cooperation system with continuous time delays and feedback controls. Nonlinear Anal., Real World Appl. 12, 34–38 (2011) CrossRefMATHMathSciNet Chen, L.J., Xie, X.D.: Permanence of an N-species cooperation system with continuous time delays and feedback controls. Nonlinear Anal., Real World Appl. 12, 34–38 (2011) CrossRefMATHMathSciNet
15.
go back to reference Chen, F.D.: Permanence of a discrete N-species cooperation system with time delays and feedback controls. Appl. Math. Comput. 186, 23–29 (2007) CrossRefMATHMathSciNet Chen, F.D.: Permanence of a discrete N-species cooperation system with time delays and feedback controls. Appl. Math. Comput. 186, 23–29 (2007) CrossRefMATHMathSciNet
16.
go back to reference Li, Y.K., Zhang, T.W.: Permanence of a discrete n-species cooperation system with time-varying delays and feedback controls. Math. Comput. Model. 53, 1320–1330 (2011) CrossRefMATH Li, Y.K., Zhang, T.W.: Permanence of a discrete n-species cooperation system with time-varying delays and feedback controls. Math. Comput. Model. 53, 1320–1330 (2011) CrossRefMATH
17.
go back to reference Fan, Y.H., Wang, L.L.: Permanence for a discrete model with feedback control and delay. Discrete Dyn. Nat. Soc. 2008, 945109 (2008) CrossRefMathSciNet Fan, Y.H., Wang, L.L.: Permanence for a discrete model with feedback control and delay. Discrete Dyn. Nat. Soc. 2008, 945109 (2008) CrossRefMathSciNet
18.
go back to reference Zhang, H.T., Li, Y.K.: Almost periodic solutions to dynamic equations on time scales. J. Egypt. Math. Soc. 21, 3–10 (2013) CrossRefMATH Zhang, H.T., Li, Y.K.: Almost periodic solutions to dynamic equations on time scales. J. Egypt. Math. Soc. 21, 3–10 (2013) CrossRefMATH
Metadata
Title
Permanence of an N-species cooperation system with time delays and feedback controls on time scales
Authors
Hongtao Zhang
Fode Zhang
Publication date
01-10-2014
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2014
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-013-0734-5

Other articles of this Issue 1-2/2014

Journal of Applied Mathematics and Computing 1-2/2014 Go to the issue

Premium Partner