63,468 research outputs found
Delay-Controlled Reactions
When the entities undergoing a chemical reaction are not available
simultaneously, the classical rate equation of a reaction or, alternatively for
the evolution of a population, should be extended by including non-Markovian
memory effects. We consider the two cases of an external feedback, realized by
fixed functions and an internal feedback originated in a self-organized manner
by the relevant concentration itself. Whereas in the first case the fixed
points are not changed, although the dynamical process is altered, the second
case offers a complete new behaviour, characterized by the existence of a time
persistent solution. Due to the feedback the reaction may lead to a finite
concentration in the stationary limit even in case of a single-species pair
annihilation process. We argue that the different cases are
similar to a coupling of additive or multiplicative noises in stochastic
processes.Comment: 18 pages, 3 figure
Brownian Molecules Formed by Delayed Harmonic Interactions
A time-delayed response of individual living organisms to information
exchanged within flocks or swarms leads to the emergence of complex collective
behaviors. A recent experimental setup by (Khadka et al 2018 Nat. Commun. 9
3864), employing synthetic microswimmers, allows to emulate and study such
behavior in a controlled way, in the lab. Motivated by these experiments, we
study a system of N Brownian particles interacting via a retarded harmonic
interaction. For , we characterize its collective behavior
analytically, by solving the pertinent stochastic delay-differential equations,
and for by Brownian dynamics simulations. The particles form
molecule-like non-equilibrium structures which become unstable with increasing
number of particles, delay time, and interaction strength. We evaluate the
entropy and information fluxes maintaining these structures and, to
quantitatively characterize their stability, develop an approximate
time-dependent transition-state theory to characterize transitions between
different isomers of the molecules. For completeness, we include a
comprehensive discussion of the analytical solution procedure for systems of
linear stochastic delay differential equations in finite dimension, and new
results for covariance and time-correlation matrices.Comment: 36 pages, 26 figures, current version: further improvements and one
correctio
Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances
This is the post print version of the article. The official published version can be obained from the link - Copyright 2009 IOP Publishing LtdThis paper is concerned with the synchronization problem for a new class of continuous time delayed complex networks with stochastic nonlinearities (randomly occurring nonlinearities), interval time-varying delays, unbounded distributed delays as well as multiple stochastic disturbances. The stochastic nonlinearities and multiple stochastic disturbances are investigated here in order to reflect more realistic dynamical behaviors of the complex networks that are affected by the noisy environment. By utilizing a new matrix functional with the idea of partitioning the lower bound h1 of the time-varying delay, we employ the stochastic analysis techniques and the properties of the Kronecker product to establish delay-dependent synchronization criteria that ensure the globally asymptotically mean-square synchronization of the addressed stochastic delayed complex networks. The sufficient conditions obtained are in the form of linear matrix inequalities (LMIs) whose solutions can be readily solved by using the standard numerical software. A numerical example is exploited to show the applicability of the proposed results.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, an International Joint Project sponsored by the Royal Society of the UK, the National 973 Program of China under Grant 2009CB320600, the National Natural Science Foundation of China under Grant 60804028, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers under Grant 200802861044, the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, and the Alexander von Humboldt Foundation of Germany
Synchronization in the presence of distributed delays
We study systems of identical coupled oscillators introducing a distribution
of delay times in the coupling. For arbitrary network topologies, we show that
the frequency and stability of the fully synchronized states depend only on the
mean of the delay distribution. However, synchronization dynamics is sensitive
to the shape of the distribution. In the presence of coupling delays, the
synchronization rate can be maximal for a specific value of the coupling
strength.Comment: 6 pages, 3 figure
Delay-dependent robust stability of stochastic delay systems with Markovian switching
In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method
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