We are honored to have this opportunity putting a special issue honoring Professor Kazuo Nishimura. Since the end of the 1970s, Kazuo has made enormous contributions to economics theory, in particular, in the field of non-linear economic dynamics. As we all know, those contributions are widely acknowledged, as is represented by his election to a fellow of the Econometric Society in 1992 and publication of the two previous special issues honoring Kazuo, the first in 2007 by Journal of Difference Equations and Applications and the second in 2012 by Macroeconomic Dynamics.1 Since those special issues appeared, the field of non-linear dynamic economics that Kazuo pioneered has become more and more important. So many young economists who might not know the days in which Kazuo’s first papers were written have joined in his field, which has become even richer. This is why we believe that it is about time to recognize his contributions to non-linear economic dynamics. The authors who gathers this occasion, as well as the editor-in-chief of the journal, Professor Bruce Mizrach, all share this view of the present guest editors for the special issue. One way or another, the papers in this special issue have all glow out of the research on which Kazuo have made pioneering impacts. As is well known, the first great contribution of Kazuo is to develop a bifurcation method in the analysis of equilibrium dynamics (Benhabib and Nishimura 1979; 1985). Since then, many studies have adopted this theory in various economic models. In this special issue, Nishimura and Shigoka (this issue) and Bosi and Desmarchelier (this issue) make interesting contributions in this field. Since those earlier contributions, Kazuo has been concerned with impatience and altruism; his early contributions include Magill and Nishimura (1984) and Benhabib, Majumdar, and Nishimura (1987). This line of studies is advanced by Clain-Chamosset-Yvrard and Seegmuller (this issue), Aoki, Nishimura, and Yano (this issue), and Fujiu and Yano (this issue). Kazuo’s important contribution in the 1990s is to demonstrate that chaotic dynamics may emerge in an optimal growth model for any level of real interest rate (Nishimura, Sorger and Yano, 1994; Nishimura and Yano 1995; 1996); whether or not that is the case is one of the important open questions in optimal growth theory. Deng, Fujio and Khan (this issue) advance Kazuo’s method further. Following this work, Kazuo made highly influential contributions to the literature on sunspot and indeterminacy (Benhabib and Nishimura, 1998; Benhabib, Meng and Nishimura, 2000). Bambi and Venditti (this issue) follows this line of work. More broadly speaking, almost all of Kazuo’s studies are concerned with the stability and instability of a dynamic economy, which Takahashi’s work addresses. Looking back the impressive contributions that Kazuo has made to economics (see Nishimura (2012)), we see strong influences of his teachers the late Professors Hirofumi Uzawa and Lionel McKenzie, who were concerned with the stability and instability of a dynamic economy. Kazuo has succeeded in integrating their works with the great contributions of his own. This special issue is based on the special session in honor of Kazuo Nishimura during The 26th Society for Nonlinear Dynamics and Econometrics. The meeting was held at Keio University in Tokyo on March 19 and 20, 2018, where more than 200 researchers from all over the world participated. The special session was chaired by Ippei Fujiwara. Three papers were presented by Liuchun Deng, Harutaka Takahshi, and Kazuo Nishimura, who contribute related papers to this issue. The titles of the presentations were as follows:

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经济模型中的商业周期和不确定性：纪念西村和夫教授的特刊

我们很荣幸有机会发表特刊以纪念西村和夫教授。自 1970 年代末以来，一夫对经济学理论做出了巨大贡献，尤其是在非线性经济动力学领域。众所周知，这些捐款被广泛承认，正如他在1992年的计量计量会议的选举中所代表的那样，并出版了以前的两个特别问题，尊重Kazuo，2007年的差异方程和申请杂志和申请2012 年由 Macroeconomic Dynamics 排名第二。1 由于这些特殊问题的出现，Kazuo 开创的非线性动态经济学领域变得越来越重要。许多可能不知道 Kazuo 撰写第一篇论文的年代的年轻经济学家加入了他的领域，这变得更加富有。这就是为什么我们认为是时候承认他对非线性经济动态的贡献了。此次聚会的作者，以及期刊主编 Bruce Mizrach 教授，都对本期特刊客座编辑持相同观点。无论如何，本期特刊中的论文都从 Kazuo 产生了开创性影响的研究中发光。众所周知，Kazuo 的第一个重大贡献是在平衡动力学分析中发展了分岔方法（Benhabib 和 Nishimura 1979；1985）。此后，许多研究在各种经济模型中采用了这一理论。在本期特刊中，Nishimura 和 Shigoka（本期）以及 Bosi 和 Desmarchelier（本期）在该领域做出了有趣的贡献。从早期的那些贡献开始，Kazuo 就一直关注不耐烦和利他主义；他的早期贡献包括 Magill 和 Nishimura（1984）以及 Benhabib、Majumdar 和 Nishimura（1987）。这一系列研究由 Clain-Chamosset-Yvrard 和 Seegmuller（本期）、Aoki、Nishimura 和矢野（本期）以及 Fujiu 和矢野（本期）提出。Kazuo 在 1990 年代的重要贡献是证明了在任何实际利率水平的最优增长模型中都可能出现混沌动力学（Nishimura、Sorger 和 Yano，1994；Nishimura 和 Yano，1995；1996）；是否如此是最优增长理论中重要的开放性问题之一。Deng、Fujio 和 Khan（本期）进一步推进了 Kazuo 的方法。继这项工作后，Kazuo 对有关太阳黑子和不确定性的文献做出了极具影响力的贡献（Benhabib 和 Nishimura，1998 年；Benhabib、Meng 和 Nishimura，2000 年）。Bambi 和 Venditti（本期）遵循这一工作。更广泛地说，几乎所有 Kazuo 的研究都关注动态经济的稳定性和不稳定性，这也是高桥的作品所解决的问题。回顾 Kazuo 对经济学做出的令人印象深刻的贡献（见 Nishimura (2012)），我们看到他的老师已故教授宇泽博文和莱昂内尔麦肯齐的强大影响，他们关注动态经济的稳定性和不稳定性。Kazuo 成功地将他们的作品与他自己的巨大贡献结合起来。本期特刊基于第 26 届非线性动力学和计量经济学会期间为纪念西村一夫而举行的特别会议。会议于2018年3月19日至20日在东京庆应义塾大学举行，来自世界各地的200多名研究人员参加了会议。特别会议由藤原一平主持。Liuchun Deng、Harutaka Takahshi 和 Kazuo Nishimura 提交了三篇论文，他们为本期贡献了相关论文。演讲题目如下：谁为此问题贡献了相关论文。演讲题目如下：谁为此问题贡献了相关论文。演讲题目如下：