New contractivity condition in a population model with piecewise constant arguments
New contractivity condition in a population model with piecewise constant arguments
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DOI：
10.1016/j.jmaa.2008.05.025
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发表时间：
2008-10
影响因子：
1.3
通讯作者：
Y. Muroya
中科院分区：
文献类型：
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作者：
Y. Muroya
在本文中，我们改进了以下带分段常数参数的微分方程的正平衡 N*=1a+Σi=0mbi 解的收缩性条件： 其中 r(t) 是 [0,+∞) 上的非负连续函数，r(t)≢0, Σi=0mbi>0, bi⩾0, i=0,1,2,…,m，并且 a+b0>Σi=1mbi。特别是，对于 a=0 和 m⩾1 的情况，我们确实改进了该模型解的已知三种类型的收缩性条件（例如，参见 [Y. Muroya, A充分条件在带有分段常量参数的逻辑方程中，Hokkaido Math. J. 32 (2003) 75–83]）。对于另一种情况a≠0且m⩾1，在Σj=1mbj−2b0<a⩽(Σj=1mbj)/(1+b0/Σj=0mbj)的条件下，得到的结果部分改进了作者给出的关于该模型正平衡解的收缩性的已知结果[Y. Muroya，分段常延迟逻辑方程中的持久性、收缩性和全局稳定性，J. Math。肛门。应用。 270 (2002) 602–635] 等。
In this paper, we improve contractivity conditions of solutions for the positive equilibrium N∗=1a+∑i=0mbiof the following differential equation with piecewise constant arguments: where r(t) is a nonnegative continuous function on [0,+∞), r(t)≢0, ∑i=0mbi>0, bi⩾0, i=0,1,2,…,m, and a+b0>∑i=1mbi. In particular, for the case a=0 and m⩾1, we really improve the known three type conditions of the contractivity for solutions of this model (see for example, [Y. Muroya, A sufficient condition on global stability in a logistic equation with piecewise constant arguments, Hokkaido Math. J. 32 (2003) 75–83]). For the other case a≠0 and m⩾1, under the condition ∑j=1mbj−2b0<a⩽(∑j=1mbj)/(1+b0/∑j=0mbj), the obtained result partially improves the known results on the contractivity of solutions for the positive equilibrium of this model given by the author [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602–635] and others.