From Coupled Dynamical Systems to Biological Irreversibility
  In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic itinerancy in high-dimensional dynamical systems is briefly reviewed, with discussion on a possible connection with a Milnor attractor network. Third, infinite-dimensional collective dynamics is studied, in the thermodynamic limit of the globally coupled map, where bifurcation to lower-dimensional attractors by the addition of noise is briefly reviewed. Following the study of coupled dynamical systems, a scenario for developmental process of cell society is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Differentiation of cell types is found as a natural consequence of such a system. "Stem cells" that either proliferate or differentiate to different types generally appear in the system, where irreversible loss of multipotency is demonstrated. Robustness of the developmental process against microscopic and macroscopic perturbations is found and explained, while irreversibility in developmental process is analyzed in terms of the gain of stability, loss of diversity and chaotic instability. Construction of a phenomenology theory for development is discussed in comparison with the thermodynamics. 
Kunihiko Kaneko