Spontaneous structure formation in a network of chaotic units with variable connection strengths

As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural order emerges even without any inter-unit synchronization of dynamics. Within this structure, units spontaneously separate into two groups whose distinguishing feature is that the first group possesses many outwardly-directed connections to the second group, while the second group possesses only few outwardly-directed connections to the first. The relevance of the results to structure formation in neural networks is briefly discussed.Comment: 4 pages, 3 figures, REVTe

Macroscopic chaos in globally coupled maps

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to the evolution of the single (or microscopic) elements of the system. The usual Lyapunov exponent is not able to capture the essential features of this macroscopic phenomenon. Using the recently introduced notion of finite size Lyapunov exponent, we characterize, in a consistent way, these macroscopic behaviours. Basically, at small values of the perturbation we recover the usual (microscopic) Lyapunov exponent, while at larger values a sort of macroscopic Lyapunov exponent emerges, which can be much smaller than the former. A quantitative characterization of the chaotic motion at hydrodynamical level is then possible, even in the absence of the explicit equations for the time evolution of the macroscopic observables.Comment: 24 pages revtex, 9 figures included. Improved version also with 1 figure and some references adde

Coupled Map Modeling for Cloud Dynamics

A coupled map model for cloud dynamics is proposed, which consists of the successive operations of the physical processes; buoyancy, diffusion, viscosity, adiabatic expansion, fall of a droplet by gravity, descent flow dragged by the falling droplet, and advection. Through extensive simulations, the phases corresponding to stratus, cumulus, stratocumulus and cumulonimbus are found, with the change of the ground temperature and the moisture of the air. They are characterized by order parameters such as the cluster number, perimeter-to-area ratio of a cloud, and Kolmogorov-Sinai entropy.Comment: 9 pages, 4 figure, LaTeX, mpeg simulations available at http://aurora.elsip.hokudai.ac.jp

Recursiveness, Switching, and Fluctuations in a Replicating Catalytic Network

A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers of molecules and species, three phases are found: fast switching state without recursive production, recursive production, and itinerancy between the above two states. The number distributions of the molecules in the recursive states are shown to be log-normal except for those species that form a core hypercycle, and are explained with the help of a heuristic argument.Comment: 4 pages (with 7 figures (6 color)), submitted to PR

State Differentiation by Transient Truncation in Coupled Threshold Dynamics

Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. Universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres

Synthetic Turing protocells: vesicle self-reproduction through symmetry-breaking instabilities

The reproduction of a living cell requires a repeatable set of chemical events to be properly coordinated. Such events define a replication cycle, coupling the growth and shape change of the cell membrane with internal metabolic reactions. Although the logic of such process is determined by potentially simple physico-chemical laws, the modeling of a full, self-maintained cell cycle is not trivial. Here we present a novel approach to the problem which makes use of so called symmetry breaking instabilities as the engine of cell growth and division. It is shown that the process occurs as a consequence of the breaking of spatial symmetry and provides a reliable mechanism of vesicle growth and reproduction. Our model opens the possibility of a synthetic protocell lacking information but displaying self-reproduction under a very simple set of chemical reactions

Origin of complexity in multicellular organisms

Through extensive studies of dynamical system modeling cellular growth and reproduction, we find evidence that complexity arises in multicellular organisms naturally through evolution. Without any elaborate control mechanism, these systems can exhibit complex pattern formation with spontaneous cell differentiation. Such systems employ a `cooperative' use of resources and maintain a larger growth speed than simple cell systems, which exist in a homogeneous state and behave 'selfishly'. The relevance of the diversity of chemicals and reaction dynamics to the growth of a multicellular organism is demonstrated. Chaotic biochemical dynamics are found to provide the multi-potency of stem cells.Comment: 6 pages, 2 figures, Physical Review Letters, 84, 6130, (2000

Condensation in Globally Coupled Populations of Chaotic Dynamical Systems

The condensation transition, leading to complete mutual synchronization in large populations of globally coupled chaotic Roessler oscillators, is investigated. Statistical properties of this transition and the cluster structure of partially condensed states are analyzed.Comment: 11 pages, 4 figures, revte

Cosmological Family Asymmetry and CP violation

We discuss how the cosmological baryon asymmetry can be achieved by the lepton family asymmetries of heavy Majorana neutrino decays and they are related to CP violation in neutrino oscillation, in the minimal seesaw model with two heavy Majorana neutrinos. We derive the most general formula for CP violation in neutrino oscillation in terms of the heavy Majorana masses and Yukawa mass term. It is shown that the formula is very useful to classify several models in which $e-$, $\mu-$ and $\tau-$leptogenesis can be separately realized and to see how they are connected with low energy CP violaton. To make the models predictive, we take texture with two zeros in the Dirac neutrino Yukawa matrix. In particular, we find some interesting cases in which CP violation in neutrino oscillation can happen while lepton family asymmetries do not exist at all. On the contrary, we can find $e-$, $\mu-$ and $\tau-$leptogenesis scenarios in which the cosmological CP violation and low energy CP violation measurable via neutrino oscillations are very closely related to each other. By determining the allowed ranges of the parameters in the models, we predict the sizes of CP violation in neutrino oscillation and $|V_{e3}^{MNS}|$. Finally, the leptonic unitarity triangles are reconstructed.Comment: 22 pages, 9 figures A figure caption correcte