Note on permanence and global stability in delayed ratio-dependent predator-prey models with monotonic functional responses

  • Authors:

  • Lin-Lin Wang;Yong-Hong Fan

  • Affiliations:

  • School of Mathematics and Information, Ludong University, Yantai, Shandong, 264025, People's Republic of China and Department of Applied Mathematics, Beijing Institute of Technology, Beijing, 1000 ...;School of Mathematics and Information, Ludong University, Yantai, Shandong, 264025, People's Republic of China and Department of Mathematics, Southeast University, Nanjing, Jiangsu, 210096, People ...

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

Sufficient conditions of the permanence and global stability for the general delayed ratio-dependent predator-prey model {x^'(t)=x(t)[a(t)-b(t)x(t)]-c(t)g(x(t)y(t))y(t),y^'(t)=y(t)[e(t)g(x(t-@t)y(t-@t))-d(t)], are obtained when the functional response function g is monotonic, where a(t),b(t),c(t),d(t) and e(t) are all positive periodic continuous functions with period @w0,@t is a positive constant. The permanence result improves Theorem 2.1 in Fan and Li (2007) [14], and the condition that guarantees the existence of positive periodic solutions for the system generalizes the corresponding result in Fan et al. (2003) [18] and Li and Wang (2006) [20]. Finally, we perform numerical simulations to support our theoretical results.