This book explains why complex systems research is important in understanding the structure, function and dynamics of complex natural and social phenomena. It illuminates how complex collective behavior emerges from the parts of a system, due to the interaction between the system and its environment. Readers will learn the basic concepts and methods of complex system research. The authors show that very different complex phenomena of nature and society can be analyzed and understood by nonlinear dynamics since many systems of very different fields, such as physics, chemistry, biology, economics, psychology and sociology have similar architecture. The book is not highly technical mathematically, but teaches and uses the basic mathematical notions of dynamical system theory, making the book useful for students of science majors and graduate courses. Still, it is intended to be readable for a more general audience, for those who ask: What really are complex systems?

1 COMPLEX SYSTEMS: THE INTELLECTUAL LANDSCAPE
1.1 The century of complexity?
1.2 Characteristics of simple and complex systems
1.2.1 System and its environment
1.2.2 Simple systems
1.2.3 Complex systems
1.3 Connecting the dots

2 HISTORY of COMPLEX SYSTEMS RESEARCH
2.1 Reductionist success stories versus the importance of
organization principles
2.1.1 Reductionism and holism in quantum physics
2.1.2 Reductionism and complexity in molecular biology
2.2 Ancestors of present day complex system research
2.2.1 Systems theory
2.2.2 Cybernetics
2.2.3 Nonlinear science in action: Theory of dissipative
structures, synergetics and catastrophe theory

3 FROM THE CLOCKWORK WORLD VIEW to IRREVERSIBILITY (and BACK?)
3.1 Cyclic universe versus linear time concept: the metaphysical
perspective
3.1.1 Cyclic Universe
3.1.2 Linear time concepts
3.2 The Newtonian Clockwork Universe
3.2.1 The mechanical clock
3.2.2 Kepler¿s integral laws
3.2.3 Newton¿s differential laws, Hamilton equations,
conservative oscillation, dissipation
3.3 Mechanics versus Thermodynamics
3.3.1 Heat conduction and irreversibility
3.3.2 Steam engine, feedback control, irreversibility
3.3.3 The first and second laws of thermodynamics
3.4 The birth of the modern theory of dynamical systems
3.5 Oscillations
3.5.1 The Lotka ¿Volterra Model
3.5.2 Stable oscillation: limit cycles
3.5.3 Quasiperiodic motions: A few words about the modern
theory of dynamical systems
3.6 The chaos paradigm: then and now
3.6.1 Defining and detecting chaos
3.6.2 Structural and geometrical conditions of chaos: what
is important and what is not?
3.6.3 The necessity of being chaotic
3.6.4 Controlling chaos: why and how?
3.6.5 Traveling to High-dimension land: Chaotic itinerancy
3.7 Direction of evolution
3.7.1 Dollös law in retrospective
3.7.2 Is something never-decreasing during evolution?
3.8 Cyclic universe: revisited. . . and criticized

4 THE DYNAMIC WORLD VIEW in ACTION
4.1 Causality, teleology and about the scope and limits of the
dynamical paradigm
4.1.1 Causal versus teleological description
4.1.2 Causality, networks, emergent novelty
4.2 Chemical kinetics: a prototype of nonlinear science
4.2.1 On the structure ¿ dynamics relationship for chemical
reactions
4.2.2 Chemical kinetics as a metalanguage
4.2.3 Spatiotemporal patterns in chemistry and biology
4.3 Systems biology: the half admitted renaissance of cybernetics
and systems theory
4.3.1 Life itself
4.3.2 Cells as self-referential systems
4.3.3 The old-new systems biology
4.3.4 Random Boolean networks: model framework and
applications for genetic networks
4.4 Population dynamic and epidemic models: biological and social
4.4.1 Connectivity, stability, diversity
4.4.2 The epidemic propagation of infections and ideas
4.4.3 Modeling social epidemics
4.5 Evolutionary dynamics
4.6 Dynamic models of war and love
4.6.1 Lanchaster¿s combat model and its variations
4.6.2 Is love different from war?
4.7 Social dynamics: some examples
4.7.1 Segregation dynamics
4.7.2 Opinion dynamics
4.8 Nonlinear dynamics in economics: some examples
4.8.1 Business cycles
4.8.2 Controlling chaos in economic models
4.9 Drug market: controlling chaos

5 THE SEARCH FOR LAWS: DEDUCTIVE VERSUS
INDUCTIVE
5.