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Mathematical problems for complex networks
Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy
is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics
Impulse-Based Hybrid Motion Control
The impulse-based discrete feedback control has been proposed in previous
work for the second-order motion systems with damping uncertainties. The
sate-dependent discrete impulse action takes place at zero crossing of one of
both states, either relative position or velocity. In this paper, the proposed
control method is extended to a general hybrid motion control form. We are
using the paradigm of hybrid system modeling while explicitly specifying the
state trajectories each time the continuous system state hits the guards that
triggers impulsive control actions. The conditions for a stable convergence to
zero equilibrium are derived in relation to the control parameters, while
requiring only the upper bound of damping uncertainties to be known. Numerical
examples are shown for an underdamped closed-loop dynamics with oscillating
transients, an upper bounded time-varying positive system damping, and system
with an additional Coulomb friction damping.Comment: 6 pages, 4 figures, IEEE conferenc
Stability analysis of impulsive stochastic CohenāGrossberg neural networks with mixed time delays
This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this paper, the problem of stability analysis for a class of impulsive stochastic CohenāGrossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic CohenāGrossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.This work was supported by the Natural Science Foundation of CQ CSTC under grant 2007BB0430, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant KJ070401, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany
Mathematical control of complex systems
Copyright Ā© 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Pulsive feedback control for stabilizing unstable periodic orbits in a nonlinear oscillator with a non-symmetric potential
We examine a strange chaotic attractor and its unstable periodic orbits in
case of one degree of freedom nonlinear oscillator with non symmetric
potential. We propose an efficient method of chaos control stabilizing these
orbits by a pulsive feedback technique. Discrete set of pulses enable us to
transfer the system from one periodic state to another.Comment: 11 pages, 4 figure
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