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Global Stability for a Coupled System of Fractional-Order Differential Equations with Discontinuous Terms on Network

  • Yang GaoEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)

Abstract

In this paper, a coupled system of fractional-order differential equations with discontinuous terms is investigated. The new model is constructed to realize the discontinuous control aim via the threshold policy (TP). Firstly, equilibrium’s existence theorems for the new model are obtained by using the algebra theory and Filippov theory. Secondly, sufficient conditions to global Mittag-Leffler stability of the equilibrium are obtained based on the new model by applying graph theoretical approach of coupled systems and Laplace transform method.

Keywords

Filippov Caputo Mittag-Leffler Global stability Threshold policy Differential inclusion 

References

  1. 1.
    Freedman, H.I., Takeuchi, Y.: Global stability and predator dynamics in a model of prey dispersal in a patchy environment. Nonlinear Anal. Theory Methods Appl. 13(8), 993–1002 (1989)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Kuang, Y., Takeuchi, Y.: Predator-prey dynamics in models of prey dispersal in 2-patch environments. Math. Biosci. 120(1), 77–98 (1994)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cui, J.G.: The effect of dispersal on permanence in a predator-prey population growth model. Comput. Math. Appl. 44(8–9), 1085–1097 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Xu, R., Chaplain, M.A.J., Davidson, F.A.: Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments. Nonlinear Anal. Real World Appl. 5(1), 183–206 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhang, L., Teng, Z.D.: Permanence for a delayed periodic predator-prey model with prey dispersal in multi-patches and predator density-independent. J. Math. Anal. Appl. 338(1), 175–193 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Li, M.Y., Shuai, Z.S.: Global-stability problem for coupled systems of differential equations on networks. J. Differ. Equ. 248(1), 1–20 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Li, H.L., Jiang, Y.L., Wang, Z.L., Zhang, L., Teng, Z.D.: Globlal Mittag-Leffler stability of coupled system of fractional-order differential equations on network. Appl. Math. Comput. 270, 269–277 (2015)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Li, H.L., Hu, C., Jiang, Y.L., Zhang, L., Teng, Z.D.: Global Mittag-Leffler stability for a coupled system of fractional-order differential equations on network with feedback controls. Neurocomputing 214, 233–241 (2016)CrossRefGoogle Scholar
  9. 9.
    Huang, L.H., Guo, Z.Y., Wang, F.J.: The theory and application for the differential equations with discontinuous right side. Science Press, Beijing (2013). (in Chinese)Google Scholar
  10. 10.
    Zhao, T.T., Xiao, Y.N., Smith, R.J.: Non-smooth plant disease models with economic thresholds. Math. Biosci. 241, 34–48 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: A Lyapunov functions for fractional order systems. Commun. Nonlinear Sci. Numer. Simulat. 19, 2951–2957 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Daqing Normal UniversityDaqingPeople’s Republic of China

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