Recent advances in discrete analysis and control of hybrid systems

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.

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Evaluation and control of opinion polarization and disagreement: a review

International Journal of Crowd Science ◽

10.1108/ijcs-02-2021-0003 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Yuejiang Li ◽

Hong Zhao

Keyword(s):

Design Methodology ◽

Crucial Importance ◽

Content Type ◽

Recent Advances ◽

And Control

Purpose The purpose of this paper is to review the recent studies on opinion polarization and disagreement. Design/methodology/approach In this work, recent advances in opinion polarization and disagreement and pay attention to how they are evaluated and controlled are reviewed. Findings In literature, three metrics: polarization, disagreement and polarization-disagreement index are usually adopted and there is a tradeoff between polarization and disagreement. Different strategies have been proposed in literature which can significantly control opinion polarization and disagreement based on these metrics. Originality/value This review is of crucial importance to summarize works on opinion polarization and disagreement and to the better understanding and control of them.

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