author : Arkady Pikovsky

Books

• Synchronization. 2001, with Michael Rosenblum, Jurgen Kurths
• Lyapunov Exponents. 2016, with Antonio Politi

Books : reviews

Arkady Pikovsky, Michael Rosenblum, Jurgen Kurths.
Synchronization: a universal concept in nonlinear sciences.
CUP. 2001

First recognized in 1665 by Christiaan Huygens, synchronization phenomena are abundant in science, nature, engineering, and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons, and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae, and is based on qualitative intuitive ideas. The main effects are illustrated with experimental examples and figures, and the historical development is also outlined. The second half of the book presents the main effects of synchronization in a rigorous and systematic manner, describing both classical results on synchronization of periodic oscillators, and recent developments in chaotic systems, large ensembles, and oscillatory media. This comprehensive book will be of interest to a broad audience, from graduate students to specialist researchers in physics, applied mathematics, engineering, and natural sciences.

Arkady Pikovsky, Antonio Politi.
Lyapunov Exponents: a tool to explore complex dynamics.
CUP. 2016

Lyapunov exponents he at the heart of chaos theory and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterisation of phenomena such as synchronisation, weak and global chaos in low and high-dimensional setups, and localisation. This text equips readers with all the investigative expertise needed to explore fully the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.