1,504 research outputs found
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
Pinning dynamic systems of networks with Markovian switching couplings and controller-node set
In this paper, we study pinning control problem of coupled dynamical systems
with stochastically switching couplings and stochastically selected
controller-node set. Here, the coupling matrices and the controller-node sets
change with time, induced by a continuous-time Markovian chain. By constructing
Lyapunov functions, we establish tractable sufficient conditions for
exponentially stability of the coupled system. Two scenarios are considered
here. First, we prove that if each subsystem in the switching system, i.e. with
the fixed coupling, can be stabilized by the fixed pinning controller-node set,
and in addition, the Markovian switching is sufficiently slow, then the
time-varying dynamical system is stabilized. Second, in particular, for the
problem of spatial pinning control of network with mobile agents, we conclude
that if the system with the average coupling and pinning gains can be
stabilized and the switching is sufficiently fast, the time-varying system is
stabilized. Two numerical examples are provided to demonstrate the validity of
these theoretical results, including a switching dynamical system between
several stable sub-systems, and a dynamical system with mobile nodes and
spatial pinning control towards the nodes when these nodes are being in a
pre-designed region.Comment: 9 pages; 3 figure
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators
driven by an external identical oscillator is studied. Based on numerical
simulations we show that by introducing additional couplings at -th
oscillators in the ring, where is an integer and is the maximum
number of synchronized oscillators in the ring with a single coupling, the
maximum number of oscillators that can be synchronized can be increased
considerably beyond the limit restricted by size instability. We also
demonstrate that there exists an exponential relation between the number of
oscillators that can support stable synchronization in the ring with the
external drive and the critical coupling strength with a scaling
exponent . The critical coupling strength is calculated by numerically
estimating the synchronization error and is also confirmed from the conditional
Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling
relation exists for couplings between the drive and the ring. Further, we
have examined the robustness of the synchronous states against Gaussian white
noise and found that the synchronization error exhibits a power-law decay as a
function of the noise intensity indicating the existence of both noise-enhanced
and noise-induced synchronizations depending on the value of the coupling
strength . In addition, we have found that shows an
exponential decay as a function of the number of additional couplings. These
results are demonstrated using the paradigmatic models of R\"ossler and Lorenz
oscillators.Comment: Accepted for Publication in Physical Review
Impulsive consensus for complex dynamical networks with nonidentical nodes and coupling time-delays
This paper investigates the problem of global consensus between a complex dynamical network (CDN) and a known goal signal by designing an impulsive consensus control scheme. The dynamical network is complex with respect to the uncertainties, nonidentical nodes, and coupling time-delays. The goal signal can be a measurable vector function or a solution of a dynamical system. By utilizing the Lyapunov function and Lyapunov-Krasovskii functional methods, robust global exponential stability criteria are derived for the error system, under which global exponential impulsive consensus is achieved for the CDN. These criteria are expressed in terms of linear matrix inequalities (LMIs) and algebraic inequalities. Thus, the impulsive controller can be easily designed by solving the derived inequalities. Meanwhile, the estimations of the consensus rate for global exponential consensus are also obtained. Two examples with numerical simulations are worked out for illustration. © 2011 Society for Industrial and Applied Mathematics.published_or_final_versio
Revealing networks from dynamics: an introduction
What can we learn from the collective dynamics of a complex network about its
interaction topology? Taking the perspective from nonlinear dynamics, we
briefly review recent progress on how to infer structural connectivity (direct
interactions) from accessing the dynamics of the units. Potential applications
range from interaction networks in physics, to chemical and metabolic
reactions, protein and gene regulatory networks as well as neural circuits in
biology and electric power grids or wireless sensor networks in engineering.
Moreover, we briefly mention some standard ways of inferring effective or
functional connectivity.Comment: Topical review, 48 pages, 7 figure
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