9,882 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
Multifractal analysis of nonhyperbolic coupled map lattices: Application to genomic sequences
Symbolic sequences generated by coupled map lattices (CMLs) can be used to
model the chaotic-like structure of genomic sequences. In this study it is
shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a
shift of 4 symbols) very closely reproduce the multifractal spectrum of
human genomic sequences for coupling constant if .
The presence of rare configurations causes deviations for , which
disappear if the rare event statistics of the CML is modified. Such rare
configurations are known to play specific functional roles in genomic sequences
serving as promoters or regulatory elements.Comment: 7 pages, 6 picture
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
Long transients and cluster size in globally coupled maps
We analyze the asymptotic states in the partially ordered phase of a system
of globally coupled logistic maps. We confirm that, regardless of initial
conditions, these states consist of a few clusters, and they properly belong in
the ordered phase of these systems. The transient times necessary to reach the
asymptotic states can be very long, especially very near the transition line
separating the ordered and the coherent phases. We find that, where two
clusters form, the distribution of their sizes corresponds to windows of
regular or narrow-band chaotic behavior in the bifurcation diagram of a system
of two degrees of freedom that describes the motion of two clusters, where the
size of one cluster acts as a bifurcation parameter.Comment: To appear in Europhysics Letter
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
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
K_l3 form factor with two-flavors of dynamical domain-wall quarks
We report on our calculation of K \to \pi vector form factor by numerical
simulations of two-flavor QCD on a 16^3x32x12 lattice at a \simeq 0.12 fm using
domain-wall quarks and DBW2 glue. Our preliminary result at a single sea quark
mass correponding to m_PS/m_V \simeq 0.53 shows a good agreement with previous
estimate in quenched QCD and that from a phenomenological model.Comment: 6 pages, 5 figures, poster presented at Lattice2005 (Weak matrix
elements); v2: a reference adde
Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps
We study the stability of the fixed-point solution of an array of mutually
coupled logistic maps, focusing on the influence of the delay times,
, of the interaction between the th and th maps. Two of us
recently reported [Phys. Rev. Lett. {\bf 94}, 134102 (2005)] that if
are random enough the array synchronizes in a spatially homogeneous
steady state. Here we study this behavior by comparing the dynamics of a map of
an array of delayed-coupled maps with the dynamics of a map with
self-feedback delayed loops. If is sufficiently large, the dynamics of a
map of the array is similar to the dynamics of a map with self-feedback loops
with the same delay times. Several delayed loops stabilize the fixed point,
when the delays are not the same; however, the distribution of delays plays a
key role: if the delays are all odd a periodic orbit (and not the fixed point)
is stabilized. We present a linear stability analysis and apply some
mathematical theorems that explain the numerical results.Comment: 14 pages, 13 figures, important changes (title changed, discussion,
figures, and references added
- …