The modern world is complex beyond human understanding and control. The science of complex systems aims to find new ways of thinking about the many interconnected networks of interaction that defy traditional approaches. Thus far, research into networks has largely been restricted to pairwise relationships represented by links between two nodes. This course marks a major extension of networks to multidimensional hypernetworks for modeling multi-element relationships, such as companies making up the stock market, the neighborhoods forming a city, people making up committees, divisions making up companies, computers making up the internet, men and machines making up armies, or robots working as teams. This course makes an important contribution to the science of complex systems by: (i) extending network theory to include dynamic relationships between many elements; (ii) providing a mathematical theory able to integrate multilevel dynamics in a coherent way; (iii) providing a new methodological approach to analyze complex systems; and (iv) illustrating the theory with practical examples in the design, management and control of complex systems taken from many areas of application.
Professor Jeff Johnson is Professor of Complexity Science and Design. He joined the Open University in 1980 after three years as Senior Research Associate in the Geography Department of Cambridge University, and six years as Research Fellow in the Mathematics Department of Essex University.
Based on the course presented at the 4th Ph.D. summer School - conference on “Mathematical Modeling of Complex Systems”, Cultural Foundation “Kritiki Estia”, 14 – 25 July, 2014, Athens - https://nlsconf.physics.uoc.gr