This book is designed to be an overview to the core concepts within complexity theory, presented in an intuitive form that should be accessible to anyone with an interest in the subject. Complexity theory is an exciting new area that is offering us a fresh perspective on many important issues, such as understanding our financial system, ecosystems, and large social organizations. The aim of this book is to bring the often abstract and sophisticated concepts of this subject down to earth and understandable in an intuitive form. After starting with an overview to complex systems science and its context, we will focus on five of the core concepts within complexity theory.
Systems Theory: We will start with three sections on systems theory and systems thinking, thus introducing you to the bigger picture of why complex systems is seen as a new paradigm in science; what exactly this new paradigm is; why we need it, and lastly how it differs from our traditional methods of scientific inquiry.
Nonlinear Systems: The terms “nonlinear science” and “complex systems” are often used interchangeably showing how essential the concept of non-linearity is to this subject. In this chapter, we draw the distinction between linear and nonlinear systems and see why it matters. The second part of this section covers the subject of chaos theory and the dynamics of nonlinear systems.
Network Theory: Networks in general have arisen in almost all fields of inquiry in the past few decades, making it one of the most active and exciting areas of scientific study. In the two sections on network theory, we will explore many different types of networks, their properties and examples in the real world, from social networks to logistics networks. This section will conclude by looking at graph theory, the mathematical foundations that lie behind networks.
Complex Adaptive Systems: CAS is increasingly being used to model a wide variety of systems, from electrical power grids to economies and cultures, as it represents a powerful new way of seeing the world. This section will also cover CAS’s close relative cybernetics and the basic concepts of adaptation and evolution. Self-organization is another one of the foundational concepts within complex systems that is proving particularly relevant to the world of the 21st century as we see collaborative self- organizing groups, such as Wikipedia and the Linux foundation, emerge. But self- organization is more than just a social phenomenon. In these two sections, we will explore how it is in fact ubiquitous in our world from the formation of fish schools to magnetization and traffic jams.
The last five sections to the book are dedicated to the application of complexity theory to various domains of science. Complexity theory has been applied to many areas from business management and anthropology to engineering and the design of healthcare systems, with its number of applications continuing to grow yearly. Here, we will just give a quick outline to four different areas that it has been successfully applied to including the social sciences, economics, engineering, and earth science.
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