Kunihiko Kaneko

Qualitative features of a one-dimensional lattice of coupled-logistic maps are investigated. First, kink-antikink patterns of 2n-periodic cycles with their period-doubling bifurcations are found. Secondly, antiferro-like structures with some kinks are observed, which show the transition from torus to chaos. Lastly, spatial intermittent structures are investigated, with the emphasis on the propagation of bursts.

Spatiotemporal intermittency is investigated in a class of coupled map lattices. Burst and laminar regions form a geometrical structure in spacetime, which is analogous to the ones found in cellular automata. Mechanism of the formation of this structure is discussed, with the study on the critical properties of the propagation speed of bursts and distribution of laminar clusters. Lyapunov spectra are calculated, which show the existence of two kinds of motions, i.e., laminar and bursts. Possibil

Studies in coupled map lattices are briefly surveyed in connection with the papers in the present focus issue.

The title statement is numerically shown for a globally coupled chaotic system. With an increasing number of elements, N, the distribution of the mean field approaches a Gaussian distribution, but the decrease of its mean-square deviation with N stops for large N. This violation of the law of large numbers is found to be caused by the emergence of a subtle coherence among elements, as is measured by the mutual information. With the inclusion of noise, the law of large numbers is restored. The me

This article lists fourteen open problems in artificial life, each of which is a grand challenge requiring a major advance on a fundamental issue for its solution. Each problem is briefly explained, and, where deemed helpful, some promising paths to its solution are indicated.

A globally coupled map lattice is investigated. A simple coding of many attractors with clustering is shown. Through the coding, the attractors are organized so that their change exhibits the period-doubling bifurcation. By a simple input on a site, we can switch among attractors and tune the strength of chaos. A threshold on the cluster size is found beyond which a peculiar ``posi-nega'' switch occurs.

Chaotic itinerancy is universal dynamics in high-dimensional dynamical systems, showing itinerant motion among varieties of low-dimensional ordered states through high-dimensional chaos. Discovery, basic features, characterization, examples, and significance of chaotic itinerancy are surveyed.

During development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Stem cells, however, keep their potential to both proliferate and differentiate. A very important issue then is to understand the characteristics that distinguish stem cells from other cell types and allow them to conduct stable proliferation and differentiation. Here, we review relevant dynamical-systems approaches to describe the state