Theory of hybrid dynamical systems and its applications to biological and medical systems
Theory of hybrid dynamical systems and its applications to biological and medical systems
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DOI：
10.1098/rsta.2010.0237
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发表时间：
2010-11-13
期刊：
影响因子：
5
通讯作者：
Suzuki, Hideyuki
中科院分区：
文献类型：
--
作者：
Aihara, Kazuyuki;Suzuki, Hideyuki
在这篇介绍性文章中，我们概述了这一主题问题的内容。这个主题问题涉及一个肥沃的地区的混合动力系统的特点是共存的连续和离散动态。现在已经知道，存在许多具有不连续性的混合动力系统，如碰撞、切换、摩擦和滑动。本文的第一个目的是讨论在动力系统理论和控制系统理论这两个主要理论领域中对混合动力系统非线性动力学的理解的最新进展。将这两个理论领域的混合动力学研究结合起来，将有助于对混合动力系统有更全面的认识。此外，混合动力系统的数学建模对于理解生物和医疗系统的非线性动力学特别重要，因为它们具有许多不连续性，例如神经元中的阈值触发放电，转录因子对基因表达的开关，细胞分裂和某些类型的前列腺癌的时间疗法。因此，第二个目标是讨论最近的应用混合动力系统在生物学和医学。因此，这个问题不仅是一般性的，作为一个调查的最新进展，在混合系统理论，但也具体介绍有趣的和刺激性的应用混合系统在生物学和医学。作为本主题的介绍，我们简要介绍了非线性动力学和数学建模的历史，混合动力系统的不同数学模型，动力系统理论和控制系统理论之间的关系，简单神经元模型及其变体中复杂行为的例子，混合动力系统在生物学和医学中的应用，作为本主题期刊文章的路线图和混合系统建模的未来方向。
In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to discuss recent developments in understanding nonlinear dynamics of hybrid dynamical systems in the two main theoretical fields of dynamical systems theory and control systems theory. A combined study of the hybrid systems dynamics in the two theoretical fields might contribute to a more comprehensive understanding of hybrid dynamical systems. In addition, mathematical modelling by hybrid dynamical systems is particularly important for understanding the nonlinear dynamics of biological and medical systems as they have many discontinuities such as threshold-triggered firing in neurons, on-off switching of gene expression by a transcription factor, division in cells and certain types of chronotherapy for prostate cancer. Hence, the second aim is to discuss recent applications of hybrid dynamical systems in biology and medicine. Thus, this Issue is not only general to serve as a survey of recent progress in hybrid systems theory but also specific to introduce interesting and stimulating applications of hybrid systems in biology and medicine. As the introduction to the topics in this Theme Issue, we provide a brief history of nonlinear dynamics and mathematical modelling, different mathematical models of hybrid dynamical systems, the relationship between dynamical systems theory and control systems theory, examples of complex behaviour in a simple neuron model and its variants, applications of hybrid dynamical systems in biology and medicine as a road map of articles in this Theme Issue and future directions of hybrid systems modelling.