Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (1): 46-52.

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QUALITATIVE ANALYSIS OF BOBWHITE QUAIL POPULATION MODEL

 LI Xian-Yi, ZHU De-Ming   

  1. Department of Mathematics and Physics, Nanhua University, Hengyang 421001, China Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Online:2003-01-06 Published:2003-01-06
  • Supported by:

    This work is supported by NNSFC(10071022), Mathemat-ical Tianyuan Foundation of China (TY10026002-01-05-03) and Shanghai Priority Academic Discipline.

Abstract:

In this paper, the qualitative behavior of solutions of the bobwhite quail pop-ulation model
xn+1 = axn +bxn(1 + xpn−k)c, n = 0, 1, · · · ,
where 0 < a < 1 < a + b, p, c 2 (0,1) and k is a nonnegative integer, is investigated.Some necessary and sufficient as well as sufficient conditions for all solutions of the modelto oscillate and some sufficient conditions for all positive solutions of the model to be nonoscillatory and the convergence of nonoscillatory solutions are derived. Furthermore,the permanence of every positive solution of the model is also showed. Many known results are improved and extended and some new results are obtained for G. Ladas’ open problems.

Key words: Population model, oscillation, convergence, permanence

CLC Number: 

  • 39A10
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