9,358 research outputs found
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
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
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
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 , and 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 , and
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
. Finally, the leptonic unitarity triangles are reconstructed.Comment: 22 pages, 9 figures A figure caption correcte
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