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In this work, we proposed a patchy predator-prey model with one patch as refuge and the other as open habitat, and incorporated prey refuge in the considered model explicitly. We applied an analytical approach to study the dynamic consequences of the simplest forms of refuge used by prey and the migration efficiency. The results have shown that the refuge… (More)
A variable coefficients predator-prey system with Holling type IV functional response incorporating stage structure for both interacting populations and time delays has been presented in this paper. By analyzing the proposed system and using the standard comparison theorem, the sufficient conditions are derived for the permanence of the considered system… (More)
Condition numbers play an important role in numerical analysis. In this paper, we consider the condition number for the weighted linear least-squares(WLS) problems min with full-row rank as well as an explicit computable expression of the condition number for weighted linear least squares problem under the condition. The results extend the earlier works of… (More)
A stage-structured predator-prey system incorporating a class of functional responses is presented in this article. By analyzing the system and using the standard comparison theorem, the sufficient conditions are derived for permanence of the system and non-permanence of predators.