Books

Short works

Books : reviews

Kunihiko Kaneko.
Theory and Applications of Coupled Map Lattices.
Wiley. 1993

The technique of the coupled map lattice (CML) is a rapidly developing field in nonlinear dynamics at present. This book gives a fully illustrative overview of current research in the field.

A CML is a dynamical system in which there is some interaction (‘coupled’) between continuous state elements, which evolve in discrete time (‘map’) and are distributed on a discrete space (‘lattice’). This book investigates both the theoretical aspects and applications of CMLs to spatially extended systems in nonlinear dynamical systems.

CMLs provide a novel approach to the study of spatiotemporal chaos, pattern formation, and nonlinear biological information processing. Applications extend to general turbulent phenomena found in fluid mechanics, plasma and solid state physics, optics, and chemical reactions. In addition, because CMLs are adaptive to semi-macroscopic conditions and are numerically efficient, they are useful tools for simulating pattern formations, nonlinear waves and biological information processing (e.g. neural nets).

The book will be of interest to theoreticians in the physical, earth and life sciences.

After the introduction and general survey (K. Kaneko), the book covers the following topics: Renormalization group, universality and scaling in dynamics of coupled map lattices (S. P, Kuznetsov); Mean-field approximations. and Perron–Frobenius equations for coupled map lattices (J. M. Houlrik and M. H. Jensen); Complex spatiotemporal dynamics of chain models for flow systems (V. S., Afraimovich and M. J. Rabinovich); Chemical waves and coupled map lattices (R. Kapral); Statistical mechanics of coupled map lattices (L. A. Bunimovich and Ya. G. Sinai)

Kunihiko Kaneko, Ichiro Tsuda.
Complex Systems: Chaos and Beyond: a constructive approach with applicatons in life sciences.
Springer. 2000

The necessity to study complex systems has been recognized in several branches of science, in particular biological science. Based on a background of physics and nonlinear dynamics, the authors propose a constructive approach and dynamic many-to-many relationship for such a study. The relevance of chaos to complex systems is discussed as a concept to overcome the antitheses between determinism and nondeterminism, order and randomness, and reductionism and holism. By presenting an information-theoretical viewpoint of chaos, phenomena and concepts in the network of chaos elements, the authors set out to find new methods to deal with biological networks, in particular the brain, and also to illustrate their constructive approach with many examples from physics, biology and information technology. While maintaining a high level of rigour, an overly complicated mathematical apparatus is avoided in order to make this book accessible, beyond the specialist level, to a wider interdisciplinary readership.

Kunihiko Kaneko.
Life: an Introduction to Complex Systems Biology.
Springer. 2006

What is life? Has molecular biology given us a satisfactory answer to this question? And if not, why, and how to carry on from there? This book examines life not from the reductionist point of view, but rather asks the question: what are the universal properties of living systems and how can one construct from there a phenomenological theory of life that leads naturally to complex processes such as reproductive cellular systems, evolution and differentiation? The presentation has been deliberately kept fairly non-technical so as to address a broad spectrum of students and researchers from the natural sciences and informatics.