Stochastic Dynamics of Complex Systems

From Glasses to Evolution

Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex — for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways.

The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the description of complex phenomena of a physical and biological nature, for example, disordered magnetic materials, superconductors and glasses, models of co-evolution in ecosystems and even of ant behaviour. These heterogeneous topics are all dealt with in detail using similar analytical techniques.

This book emphasizes the unity of complex dynamics and provides the tools needed to treat a large number of complex systems of current interest. The ideas and the approach to complex dynamics it presents have not appeared in book form until now.

Contents:

• Complex Dynamics: Tools and Applications:

  • Characterization of Collective Dynamics
  • Markovian Stochastic Processes
  • Monte Carlo Methods
  • Record Statistics and Extremal Statistics
  • Complexity and Hierarchies
  • Energy Landscapes
  • Record Dynamics and Marginal Stability

• Complex Systems with Similar Dynamics:

  • Ageing of Spin Glasses
  • Magnetic Relaxation in Superconductors
  • Ageing of Colloids
  • Evolving Biological Systems
  • Non-stationary Ageing Dynamics in Ant Societies

• Epilogue:

  • What is Complexity Science?

Readership: Graduates and researchers with an interest in complex systems.
Key Features:

• No book focusing on dynamics of complex systems exist
• This is the first book emphasizing non-stationary and evolution in complex systems
• It is self-contained and presents both theory and applications