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Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System

Author

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  • Yong-Hui Xia
  • Xiang Gu
  • Patricia J. Y. Wong
  • Syed Abbas

Abstract

This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M -predators and N -preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in terms of spectral radius of explicit matrices which are much different from the conditions given by the algebraic inequalities. Finally, an example is given to show the feasibility of our results.

Suggested Citation

  • Yong-Hui Xia & Xiang Gu & Patricia J. Y. Wong & Syed Abbas, 2012. "Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, October.
    • Handle: RePEc:hin:jnlaaa:940287
    DOI: 10.1155/2012/940287
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    Cited by:

    1. Shekhar Singh Negi & Syed Abbas & Muslim Malik, 2020. "Periodic Solutions of the N-Preys and M-Predators Model with Variable Rates on Time Scales," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 945-967, September.

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