<i>M</i>関数を用いた飽和形不変集合をもつ一般化ボルテラ方程式の安定解析

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タイトル別名
  • Stability Analysis of Generalized Volterra Equation with Saturated Invariant Set with the Aid of <i>M</i>-Function
  • M関数を用いた飽和形不変集合をもつ一般化ボルテラ方程式の安定解析
  • M カンスウ オ モチイタ ホウワケイ フヘン シュウゴウ オ モツ イッパン
  • Stability Analysis of Generalized Volterra Equation with Saturated Invariant Set with the Aid of M-Function

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抄録

The object of this paper is to extend the condition presented in the previous paper for the stability of the equilibrium point of the generalized Volterra equations. In the previous paper, we proved that if the vector function describing the growth rate of species is an M-function and if the invariant set of this function is not bounded for any variable and contains the original point then the equilibrium point is globaly asymptotically stable.<br>In this paper characteristics of M-functions and of more general skew-decreasing functions are studied. It is proved that for the global asymptotic stability of the equilibrium point of the generalized Volterra equation to be an M-function for the growth-rate function is a sufficient condition without any serious restriction.

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