Phase Space Projection of Dynamical Systems

2020 ◽  
Vol 39 (3) ◽  
pp. 253-264
Author(s):  
Nemanja Bartolovic ◽  
Markus Gross ◽  
Tobias Günther
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Space Projection

Generalized canonical quantization of dynamical systems with constraints and curved phase space

1990 ◽  
Vol 332 (3) ◽  
pp. 723-736 ◽  
Author(s):  
I.A. Batalin ◽  
E.S. Fradkin ◽  
T.E. Fradkina
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Canonical Quantization

A Dynamical Systems Approach to Failure Prognosis

2004 ◽  
Vol 126 (1) ◽  
pp. 2-8 ◽  
Author(s):  
David Chelidze ◽  
Joseph P. Cusumano
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Damage Evolution ◽  
Systems Approach ◽  
Remaining Useful Life ◽  
Electromechanical System ◽  
Time To Failure ◽  
Damage Tracking ◽  
Failure Prognosis ◽  
Short Time

In this paper, a previously published damage tracking method is extended to provide failure prognosis, and applied experimentally to an electromechanical system with a failing supply battery. The method is based on a dynamical systems approach to the problem of damage evolution. In this approach, damage processes are viewed as occurring in a hierarchical dynamical system consisting of a “fast,” directly observable subsystem coupled to a “slow,” hidden subsystem describing damage evolution. Damage tracking is achieved using a two-time-scale modeling strategy based on phase space reconstruction. Using the reconstructed phase space of the reference (undamaged) system, short-time predictive models are constructed. Fast-time data from later stages of damage evolution of a given system are collected and used to estimate a tracking function by calculating the short time reference model prediction error. In this paper, the tracking metric based on these estimates is used as an input to a nonlinear recursive filter, the output of which provides continuous refined estimates of the current damage (or, equivalently, health) state. Estimates of remaining useful life (or, equivalently, time to failure) are obtained recursively using the current damage state estimates under the assumption of a particular damage evolution model. The method is experimentally demonstrated using an electromechanical system, in which mechanical vibrations of a cantilever beam are dynamically coupled to electrical oscillations in an electromagnet circuit. Discharge of a battery powering the electromagnet (the “damage” process in this case) is tracked using strain gauge measurements from the beam. The method is shown to accurately estimate both the battery state and the time to failure throughout virtually the entire experiment.

The dynamics of language

1999 ◽  
Vol 22 (2) ◽  
pp. 284-285
Author(s):  
Peter W. Culicover ◽  
Andrzej Nowak
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Simple Model ◽  
Syntactic Structure ◽  
Neural Assemblies ◽  
Systems Perspective ◽  
Model Based ◽  
Associative Structures

To deal with syntactic structure, one needs to go beyond a simple model based on associative structures, and to adopt a dynamical systems perspective, where each phrase and sentence of a language is represented as a trajectory in a syntactic phase space. Neural assemblies could possibly be used to produce dynamics that in principle could handle syntax along these lines.

DYNAMICAL ASPECTS OF INTERACTION NETWORKS

2005 ◽  
Vol 15 (11) ◽  
pp. 3467-3480 ◽  
Author(s):  
G. NICOLIS ◽  
A. GARCÍA CANTÚ ◽  
C. NICOLIS
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Stochastic Processes ◽  
Lyapunov Exponents ◽  
Network Theory ◽  
Finite Size ◽  
Interaction Networks ◽  
Deterministic Systems ◽  
Connectivity Patterns ◽  
Probabilistic Process

A connection between dynamical systems and network theory is outlined based on a mapping of the dynamics into a discrete probabilistic process, whereby the phase space is partitioned into finite size cells. It is found that the connectivity patterns of networks generated by deterministic systems can be related to the indicators of the dynamics such as local Lyapunov exponents. The procedure is extended to networks generated by stochastic processes.

Dynamics of Thermoacoustic Oscillations Leading to Lean Flame Blowout

2012 ◽  
Author(s):  
Lipika Kabiraj ◽  
R. I. Sujith
Keyword(s):  
Time Series ◽  
Steady State ◽  
Phase Space ◽  
Dynamical Systems ◽  
Nonlinear Oscillation ◽  
Bifurcation Analysis ◽  
Nonlinear Time Series Analysis ◽  
Pressure Oscillations ◽  
Reconstructed Phase Space ◽  
Thermoacoustic Oscillations

Lean flame blowout induced by thermoacoustic oscillations is a serious problem faced by the power and propulsion industry. We analyze a prototypical thermoacoustic system through systematic bifurcation analysis and find that starting from a steady state, this system exhibits successive bifurcations resulting in complex nonlinear oscillation states, eventually leading to flame blowout. To understand the observed bifurcations, we analyze the oscillation states using nonlinear time series analysis, particularly through the representation of pressure oscillations on a reconstructed phase space. Prior to flame blowout, a bursting phenomenon is observed in pressure oscillations. These burst oscillations are found to exhibit similarities with the phenomenon known as intermittency in the dynamical systems theory. This investigation based on nonlinear analysis of experimentally acquired data from a thermoacoustic system sheds light on how thermoacoustic oscillations lead to flame blowout.

CHAOTIC DIFFUSION IN MULTIDIMENSIONAL CONSERVATIVE MAPS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250237 ◽  
Author(s):  
PABLO M. CINCOTTA ◽  
CLAUDIA M. GIORDANO
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Resonance Interaction ◽  
Chaotic Diffusion ◽  
Conservative Systems

In the present paper, we provide results and discussions concerning the processes that lead to local and global chaotic diffusion in the phase space of multidimensional conservative systems. We investigate and provide a measure of the extent of the domain over which diffusion may occur. All these issues are thoroughly discussed by dealing with a multidimensional conservative map that would be representative of the dynamics of a resonance interaction, which is an important mechanism in many dynamical systems.

scholarly journals Invariant Poisson–Nijenhuis structures on Lie groups and classification

2018 ◽  
Vol 15 (04) ◽  
pp. 1850059 ◽  
Author(s):  
Zohreh Ravanpak ◽  
Adel Rezaei-Aghdam ◽  
Ghorbanali Haghighatdoost
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Symmetry Group ◽  
Lie Groups ◽  
Lie Algebras ◽  
Lie Group ◽  
Text Structure ◽  
Baxter Equation ◽  
Text Structures ◽  
Group A

We study right-invariant (respectively, left-invariant) Poisson–Nijenhuis structures ([Formula: see text]-[Formula: see text]) on a Lie group [Formula: see text] and introduce their infinitesimal counterpart, the so-called r-n structures on the corresponding Lie algebra [Formula: see text]. We show that [Formula: see text]-[Formula: see text] structures can be used to find compatible solutions of the classical Yang–Baxter equation (CYBE). Conversely, two compatible [Formula: see text]-matrices from which one is invertible determine an [Formula: see text]-[Formula: see text] structure. We classify, up to a natural equivalence, all [Formula: see text]-matrices and all [Formula: see text]-[Formula: see text] structures with invertible [Formula: see text] on four-dimensional symplectic real Lie algebras. The result is applied to show that a number of dynamical systems which can be constructed by [Formula: see text]-matrices on a phase space whose symmetry group is Lie group a [Formula: see text], can be specifically determined.

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