Global dynamics of a discretized SIRS epidemic model with time delay

AbstractWe derive a discretized SIRS epidemic model with time delay by applying a nonstandard finite difference scheme. Sufficient conditions for the global dynamics of the solution are obtained by improvements in discretization and applying proofs for continuous epidemic models. These conditions for our discretized model are the same as for the original continuous model

Convergence of a Logistic Type Ultradiscrete Model

We derive a piecewise linear difference equation from logistic equations with time delay by ultradiscretization. The logistic equation that we consider in this paper has been shown to be globally stable in the continuous and discrete time formulations. Here, we study if ultradiscretization preserves the global stability property, analyzing the asymptotic behaviour of the obtained piecewise linear difference equation. It is shown that our piecewise linear difference equation has a threshold property concerning global attractivity of equilibria, similar to the stable logistic equations with time delay

An asymptotic analysis for an integrable variant of the Lotka-Volterra prey-predator model via a determinant expansion technique

Abstract: The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka-Volterra (dhLV) system, which is an integrable variant of the famous prey-predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant

帯行列の固有値を計算する離散可積分系について

九州大学応用力学研究所研究集会報告 No.21ME-S7 「非線形波動研究の現状と将来 : 次の10 年への展望」RIAM Symposium No.21ME-S7 Current and Future Research on Nonlinear Waves : Perspectives for the Next Decade離散可積分系に分類される離散ハングリーロトカ・ボルテラ系及び離散ハングリー戸田方程式の時間発展は，あるクラスの帯行列の相似変形を与える。この性質を利用して定式化された帯行列の固有値計算アルゴリズムを紹介する

箱に番号が付いた新しい箱玉系について

九州大学応用力学研究所研究集会報告 No.25AO-S2 「非線形波動研究の拡がり」Reports of RIAM Symposium No.25AO-S2 The breadth and depth of nonlinear wave scienceProceedings of a symposium held at Chikushi Campus, Kyushu Universiy, Kasuga, Fukuoka, Japan, October 31 - November 2, 2013離散ハングリー戸田方程式の超離散版は玉に番号が付いた箱玉系の運動方程式として知られている．本報告では，離散ハングリー戸田方程式のある変形版を導入し，その超離散化を通じて箱を番号付けで区別した新しい箱玉系を導く．また，離散ハングリー戸田方程式の変形版の保存量を求め，その超離散化によって新しい箱玉系の保存量を明らかにする．保存量を求める過程において，離散ハングリーロトカ・ボルテラ系と離散ハングリー戸田方程式の変形版を結ぶベックルント変換も示す．さらに，玉に番号が付いた箱玉系と新しい箱玉系の関係についても述べる

Convergence of a Logistic Type Ultradiscrete Model

We derive a piecewise linear difference equation from logistic equations with time delay by ultradiscretization. The logistic equation that we consider in this paper has been shown to be globally stable in the continuous and discrete time formulations. Here, we study if ultradiscretization preserves the global stability property, analyzing the asymptotic behaviour of the obtained piecewise linear difference equation. It is shown that our piecewise linear difference equation has a threshold property concerning global attractivity of equilibria, similar to the stable logistic equations with time delay