13,389 research outputs found
Diversity, Stability, Recursivity, and Rule Generation in Biological System: Intra-inter Dynamics Approach
Basic problems for the construction of a scenario for the Life are discussed.
To study the problems in terms of dynamical systems theory, a scheme of
intra-inter dynamics is presented. It consists of internal dynamics of a unit,
interaction among the units, and the dynamics to change the dynamics itself,
for example by replication (and death) of units according to their internal
states. Applying the dynamics to cell differentiation, isologous
diversification theory is proposed. According to it, orbital instability leads
to diversified cell behaviors first. At the next stage, several cell types are
formed, first triggered by clustering of oscillations, and then as attracting
states of internal dynamics stabilized by the cell-to-cell interaction. At the
third stage, the differentiation is determined as a recursive state by cell
division. At the last stage, hierarchical differentiation proceeds, with the
emergence of stochastic rule for the differentiation to sub-groups, where
regulation of the probability for the differentiation provides the diversity
and stability of cell society. Relevance of the theory to cell biology is
discussed.Comment: 19 pages, Int.J. Mod. Phes. B (in press
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
Dynamics of Coupling Functions in Globally Coupled Maps: Size, Periodicity and Stability of Clusters
It is shown how different globally coupled map systems can be analyzed under
a common framework by focusing on the dynamics of their respective global
coupling functions. We investigate how the functional form of the coupling
determines the formation of clusters in a globally coupled map system and the
resulting periodicity of the global interaction. The allowed distributions of
elements among periodic clusters is also found to depend on the functional form
of the coupling. Through the analogy between globally coupled maps and a single
driven map, the clustering behavior of the former systems can be characterized.
By using this analogy, the dynamics of periodic clusters in systems displaying
a constant global coupling are predicted; and for a particular family of
coupling functions, it is shown that the stability condition of these clustered
states can straightforwardly be derived.Comment: 12 pp, 5 figs, to appear in PR
Differentiation and Replication of Spots in a Reaction Diffusion System with Many Chemicals
The replication and differentiation of spots in reaction diffusion equations
are studied by extending the Gray-Scott model with self-replicating spots to
include many degrees of freedom needed to model systems with many chemicals. By
examining many possible reaction networks, the behavior of this model is
categorized into three types: replication of homogeneous fixed spots,
replication of oscillatory spots, and differentiation from `m ultipotent
spots'. These multipotent spots either replicate or differentiate into other
types of spots with different fixed-point dynamics, and as a result, an
inhomogeneous pattern of spots is formed. This differentiation process of spots
is analyzed in terms of the loss of chemical diversity and decrease of the
local Kolmogorov-Sinai entropy. The relevance of the results to developmental
cell biology and stem cells is also discussed.Comment: 8 pages, 12 figures, Submitted to EP
Self-organized and driven phase synchronization in coupled maps
We study the phase synchronization and cluster formation in coupled maps on
different networks. We identify two different mechanisms of cluster formation;
(a) {\it Self-organized} phase synchronization which leads to clusters with
dominant intra-cluster couplings and (b) {\it driven} phase synchronization
which leads to clusters with dominant inter-cluster couplings. In the novel
driven synchronization the nodes of one cluster are driven by those of the
others. We also discuss the dynamical origin of these two mechanisms for small
networks with two and three nodes.Comment: 4 pages including 2 figure
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
Detailed Measurements of Characteristic Profiles of Magnetic Diffuse Scattering in ErBC
Detailed neutron diffraction measurements on a single crystalline
ErBC were performed. We observed magnetic diffuse scattering which
consists of three components just above the transition temperatures, which is
also observed in characteristic antiferroquadrupolar ordering compounds
HoBC and TbBC. The result of this experiments indicates that
the antiferroquadrupolar interaction is not dominantly important as a origin of
the magnetic diffuse scattering.Comment: 5 pages, 5 figures, submitted to J. Phys. Soc. Jp
Heterogeneity Induced Order in Globally Coupled Chaotic Systems
Collective behavior is studied in globally coupled maps with distributed
nonlinearity. It is shown that the heterogeneity enhances regularity in the
collective dynamics. Low-dimensional quasiperiodic motion is often found for
the mean-field, even if each element shows chaotic dynamics. The mechanism of
this order is due to the formation of an internal bifurcation structure, and
the self-consistent dynamics between the structures and the mean-field.
Keywords: Globally Coupled Map with heterogeneity, Collective behaviorComment: 11 pages (Revtex) + 4 figures (PostScript,tar+gzip
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
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