11,249 research outputs found
Delay induced Turing-like waves for one species reaction-diffusion model on a network
A one species time-delay reaction-diffusion system defined on a complex
networks is studied. Travelling waves are predicted to occur as follows a
symmetry breaking instability of an homogenous stationary stable solution,
subject to an external non homogenous perturbation. These are generalized
Turing-like waves that materialize in a single species populations dynamics
model, as the unexpected byproduct of the imposed delay in the diffusion part.
Sufficient conditions for the onset of the instability are mathematically
provided by performing a linear stability analysis adapted to time delayed
differential equation. The method here developed exploits the properties of the
Lambert W-function. The prediction of the theory are confirmed by direct
numerical simulation carried out for a modified version of the classical Fisher
model, defined on a Watts-Strogatz networks and with the inclusion of the
delay
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
Dichotomy results for delay differential equations with negative Schwarzian
We gain further insight into the use of the Schwarzian derivative to obtain
new results for a family of functional differential equations including the
famous Wright's equation and the Mackey-Glass type delay differential
equations. We present some dichotomy results, which allow us to get easily
computable bounds of the global attractor. We also discuss related conjectures,
and formulate new open problems.Comment: 16 pages, submitted to Chaos,Solitons,Fractal
Laser Chimeras as a paradigm for multi-stable patterns in complex systems
Chimera is a rich and fascinating class of self-organized solutions developed
in high dimensional networks having non-local and symmetry breaking coupling
features. Its accurate understanding is expected to bring important insight in
many phenomena observed in complex spatio-temporal dynamics, from living
systems, brain operation principles, and even turbulence in hydrodynamics. In
this article we report on a powerful and highly controllable experiment based
on optoelectronic delayed feedback applied to a wavelength tunable
semiconductor laser, with which a wide variety of Chimera patterns can be
accurately investigated and interpreted. We uncover a cascade of higher order
Chimeras as a pattern transition from N to N - 1 clusters of chaoticity.
Finally, we follow visually, as the gain increases, how Chimera is gradually
destroyed on the way to apparent turbulence-like system behaviour.Comment: 7 pages, 6 figure
A novel pseudo-random number generator based on discrete chaotic iterations
Security of information transmitted through the Internet, against passive or
active attacks is an international concern. The use of a chaos-based
pseudo-random bit sequence to make it unrecognizable by an intruder, is a field
of research in full expansion. This mask of useful information by modulation or
encryption is a fundamental part of the TLS Internet exchange protocol. In this
paper, a new method using discrete chaotic iterations to generate pseudo-random
numbers is presented. This pseudo-random number generator has successfully
passed the NIST statistical test suite (NIST SP800-22). Security analysis shows
its good characteristics. The application for secure image transmission through
the Internet is proposed at the end of the paper.Comment: The First International Conference on Evolving Internet:Internet 2009
pp.71--76 http://dx.doi.org/10.1109/INTERNET.2009.1
On the Oscillation of the Generalized Food-Limited Equations with Delay
- The objective of the paper is to find conditions for the oscillation of the food-limited equation. We established conditions for the oscillation of all solutions of the generalized foodlimited equation by transforming the equation to a non-linear delay differential equation and then to a scalar delay differential equation and using the property of the scalar delay differential equation to obtain our result. Similarly we establish conditions for the oscillation of all solutions of the foodlimited equation with several delays by transforming the equation to a scalar differential equation to obtain the oscillatory property
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