5,445 research outputs found
Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli
The collective dynamics of coupled two-dimensional chaotic maps on complex
networks is known to exhibit a rich variety of emergent properties which
crucially depend on the underlying network topology. We investigate the
collective motion of Chirikov standard maps interacting with time delay through
directed links of Gene Regulatory Network of bacterium Escherichia Coli.
Departures from strongly chaotic behavior of the isolated maps are studied in
relation to different coupling forms and strengths. At smaller coupling
intensities the network induces stable and coherent emergent dynamics. The
unstable behavior appearing with increase of coupling strength remains confined
within a connected sub-network. For the appropriate coupling, network exhibits
statistically robust self-organized dynamics in a weakly chaotic regime
Discrete Dynamical Systems Embedded in Cantor Sets
While the notion of chaos is well established for dynamical systems on
manifolds, it is not so for dynamical systems over discrete spaces with
variables, as binary neural networks and cellular automata. The main difficulty
is the choice of a suitable topology to study the limit . By
embedding the discrete phase space into a Cantor set we provided a natural
setting to define topological entropy and Lyapunov exponents through the
concept of error-profile. We made explicit calculations both numerical and
analytic for well known discrete dynamical models.Comment: 36 pages, 13 figures: minor text amendments in places, time running
top to bottom in figures, to appear in J. Math. Phy
Non-Markov stochastic dynamics of real epidemic process of respiratory infections
The study of social networks and especially of the stochastic dynamics of the
diseases spread in human population has recently attracted considerable
attention in statistical physics. In this work we present a new statistical
method of analyzing the spread of epidemic processes of grippe and acute
respiratory track infections (ARTI) by means of the theory of discrete
non-Markov stochastic processes. We use the results of our last theory (Phys.
Rev. E 65, 046107 (2002)) to study statistical memory effects, long - range
correlation and discreteness in real data series, describing the epidemic
dynamics of human ARTI infections and grippe. We have carried out the
comparative analysis of the data of the two infections (grippe and ARTI) in one
of the industrial districts of Kazan, one of the largest cities of Russia. The
experimental data are analyzed by the power spectra of the initial time
correlation function and the memory functions of junior orders, the phase
portraits of the four first dynamic variables, the three first points of the
statistical non-Markov parameter and the locally averaged kinetic and
relaxation parameters. The received results give an opportunity to provide
strict quantitative description of the regular and stochastic components in
epidemic dynamics of social networks taking into account their time
discreteness and effects of statistical memory. They also allow to reveal the
degree of randomness and predictability of the real epidemic process in the
specific social network.Comment: 18 pages, 8figs, 1 table
Follow the fugitive: an application of the method of images to open dynamical systems
Borrowing and extending the method of images we introduce a theoretical
framework that greatly simplifies analytical and numerical investigations of
the escape rate in open dynamical systems. As an example, we explicitly derive
the exact size- and position-dependent escape rate in a Markov case for holes
of finite size. Moreover, a general relation between the transfer operators of
closed and corresponding open systems, together with the generating function of
the probability of return to the hole is derived. This relation is then used to
compute the small hole asymptotic behavior, in terms of readily calculable
quantities. As an example we derive logarithmic corrections in the second order
term. Being valid for Markov systems, our framework can find application in
information theory, network theory, quantum Weyl law and via Ulam's method can
be used as an approximation method in more general dynamical systems.Comment: 9 pages, 1 figur
Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model
We study the long time behaviour of the transient before the collapse on the
periodic attractors of a discrete deterministic asymmetric neural networks
model. The system has a finite number of possible states so it is not possible
to use the term chaos in the usual sense of sensitive dependence on the initial
condition. Nevertheless, at varying the asymmetry parameter, , one observes
a transition from ordered motion (i.e. short transients and short periods on
the attractors) to a ``complex'' temporal behaviour. This transition takes
place for the same value at which one has a change for the mean
transient length from a power law in the size of the system () to an
exponential law in . The ``complex'' behaviour during the transient shows
strong analogies with the chaotic behaviour: decay of temporal correlations,
positive Shannon entropy, non-constant Renyi entropies of different orders.
Moreover the transition is very similar to that one for the intermittent
transition in chaotic systems: scaling law for the Shannon entropy and strong
fluctuations of the ``effective Shannon entropy'' along the transient, for .Comment: 18 pages + 6 figures, TeX dialect: Plain TeX + IOP macros (included
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Effect of small-world topology on wave propagation on networks of excitable elements
We study excitation waves on a Newman-Watts small-world network model of
coupled excitable elements. Depending on the global coupling strength, we find
differing resilience to the added long-range links and different mechanisms of
propagation failure. For high coupling strengths, we show agreement between the
network and a reaction-diffusion model with additional mean-field term.
Employing this approximation, we are able to estimate the critical density of
long-range links for propagation failure.Comment: 19 pages, 8 figures and 5 pages supplementary materia
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