Application of Mawhin′s Coincidence Degree and Matrix Spectral Theory to a Delayed System | Zendy

Yonghui Xia | Zendy; Xiang Lin Gu | Zendy; Patricia J. Y. Wong | Zendy; Syed Abbas | Zendy

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

Author(s) -

Yonghui Xia,

Xiang Lin Gu,

Patricia J. Y. Wong,

Syed Abbas

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/940287

Subject(s) - mathematics , coincidence , spectral radius , degree (music) , stability (learning theory) , algebraic number , matrix (chemical analysis) , spectral properties , mathematical analysis , pure mathematics , eigenvalues and eigenvectors , medicine , physics , alternative medicine , materials science , pathology , acoustics , composite material , computational chemistry , chemistry , quantum mechanics , machine learning , computer science

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

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