88,541 research outputs found
Stability and Control of Power Systems using Vector Lyapunov Functions and Sum-of-Squares Methods
Recently sum-of-squares (SOS) based methods have been used for the stability
analysis and control synthesis of polynomial dynamical systems. This analysis
framework was also extended to non-polynomial dynamical systems, including
power systems, using an algebraic reformulation technique that recasts the
system's dynamics into a set of polynomial differential algebraic equations.
Nevertheless, for large scale dynamical systems this method becomes
inapplicable due to its computational complexity. For this reason we develop a
subsystem based stability analysis approach using vector Lyapunov functions and
introduce a parallel and scalable algorithm to infer the stability of the
interconnected system with the help of the subsystem Lyapunov functions.
Furthermore, we design adaptive and distributed control laws that guarantee
asymptotic stability under a given external disturbance. Finally, we apply this
algorithm for the stability analysis and control synthesis of a network
preserving power system.Comment: to appear at the 14th annual European Control Conferenc
Network analysis of chaotic dynamics in fixed-precision digital domain
When implemented in the digital domain with time, space and value discretized
in the binary form, many good dynamical properties of chaotic systems in
continuous domain may be degraded or even diminish. To measure the dynamic
complexity of a digital chaotic system, the dynamics can be transformed to the
form of a state-mapping network. Then, the parameters of the network are
verified by some typical dynamical metrics of the original chaotic system in
infinite precision, such as Lyapunov exponent and entropy. This article reviews
some representative works on the network-based analysis of digital chaotic
dynamics and presents a general framework for such analysis, unveiling some
intrinsic relationships between digital chaos and complex networks. As an
example for discussion, the dynamics of a state-mapping network of the Logistic
map in a fixed-precision computer is analyzed and discussed.Comment: 5 pages, 9 figure
Dynamical principles in neuroscience
Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA
Controllability and observability of grid graphs via reduction and symmetries
In this paper we investigate the controllability and observability properties
of a family of linear dynamical systems, whose structure is induced by the
Laplacian of a grid graph. This analysis is motivated by several applications
in network control and estimation, quantum computation and discretization of
partial differential equations. Specifically, we characterize the structure of
the grid eigenvectors by means of suitable decompositions of the graph. For
each eigenvalue, based on its multiplicity and on suitable symmetries of the
corresponding eigenvectors, we provide necessary and sufficient conditions to
characterize all and only the nodes from which the induced dynamical system is
controllable (observable). We discuss the proposed criteria and show, through
suitable examples, how such criteria reduce the complexity of the
controllability (respectively observability) analysis of the grid
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Background: Many biological systems are modeled qualitatively with discrete
models, such as probabilistic Boolean networks, logical models, Petri nets, and
agent-based models, with the goal to gain a better understanding of the system.
The computational complexity to analyze the complete dynamics of these models
grows exponentially in the number of variables, which impedes working with
complex models. Although there exist sophisticated algorithms to determine the
dynamics of discrete models, their implementations usually require
labor-intensive formatting of the model formulation, and they are oftentimes
not accessible to users without programming skills. Efficient analysis methods
are needed that are accessible to modelers and easy to use. Method: By
converting discrete models into algebraic models, tools from computational
algebra can be used to analyze their dynamics. Specifically, we propose a
method to identify attractors of a discrete model that is equivalent to solving
a system of polynomial equations, a long-studied problem in computer algebra.
Results: A method for efficiently identifying attractors, and the web-based
tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other
analysis methods for discrete models. ADAM converts several discrete model
types automatically into polynomial dynamical systems and analyzes their
dynamics using tools from computer algebra. Based on extensive experimentation
with both discrete models arising in systems biology and randomly generated
networks, we found that the algebraic algorithms presented in this manuscript
are fast for systems with the structure maintained by most biological systems,
namely sparseness, i.e., while the number of nodes in a biological network may
be quite large, each node is affected only by a small number of other nodes,
and robustness, i.e., small number of attractors
Dynamical models of the mammalian target of rapamycin network in ageing
Phd ThesisThe mammalian Target of Rapamycin (mTOR)kinase is a central regulator of
cellular growth and metabolism and plays an important role in ageing and age-
related diseases. The increase of invitro data collected to extend our knowledge
on its regulation, and consequently improve drug intervention,has highlighted
the complexity of the mTOR network. This complexity is also aggravated by
the intrinsic time-dependent nature of cellular regulatory network cross-talks and
feedbacks. Systems biology constitutes a powerful tool for mathematically for-
malising biological networks and investigating such dynamical properties.
The present work discusses the development of three dynamical models of the
mTOR network. The first aimed at the analysis of the current literature-based
hypotheses of mTOR Complex2(mTORC2)regulation. For each hypothesis, the
model predicted specific differential dynamics which were systematically tested
by invitro experiments. Surprisingly, nocurrent hypothesis could explain the
data and a new hypothesis of mTORC2 activation was proposed.The second
model extended the previous one with an AMPK module. In this study AMPK
was reported to be activated by insulin. Using a hypothesis ranking approach
based on model goodness-of-fit, AMPK activity was insilico predicted and in
vitro tested to be activated by the insulin receptor substrate(IRS).Finally,the
last model linked mTOR with the oxidative stress response, mitochondrial reg-
ulation, DNA damage and FoxO transcription factors. This work provided the
characterisation of a dynamical mechanism to explain the state transition from
normal to senescent cells and their reversibility of the senescentphenotype.European Council 6FP
NoE LifeSpan, School of the
Faculty of Medical Sciences, Newcastle Universit
Generalized network density matrices for analysis of multiscale functional diversity
The network density matrix formalism allows for describing the dynamics of
information on top of complex structures and it has been successfully used to
analyze from system's robustness to perturbations to coarse graining multilayer
networks from characterizing emergent network states to performing multiscale
analysis. However, this framework is usually limited to diffusion dynamics on
undirected networks. Here, to overcome some limitations, we propose an approach
to derive density matrices based on dynamical systems and information theory,
that allows for encapsulating a much wider range of linear and non-linear
dynamics and richer classes of structure, such as directed and signed ones. We
use our framework to study the response to local stochastic perturbations of
synthetic and empirical networks, including neural systems consisting of
excitatory and inhibitory links and gene-regulatory interactions. Our findings
demonstrate that topological complexity does not lead, necessarily, to
functional diversity -- i.e., complex and heterogeneous response to stimuli or
perturbations. Instead, functional diversity is a genuine emergent property
which cannot be deduced from the knowledge of topological features such as
heterogeneity, modularity, presence of asymmetries or dynamical properties of a
system
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