scholarly journals A practical method for estimating coupling functions in complex dynamical systems

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190015 ◽  
Author(s):  
Isao T. Tokuda ◽  
Zoran Levnajic ◽  
Kazuyoshi Ishimura
Keyword(s):  
Social Sciences ◽  
Natural Frequencies ◽  
Network Connectivity ◽  
Electric Circuit ◽  
Practical Method ◽  
Van Der Pol ◽  
Dynamical Interaction ◽  
Measured Time ◽  
Coupling Equations ◽  
General Limit

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One such earlier attempt (Tokuda et al. 2007 Phys. Rev. Lett. 99 , 064101. ( doi:10.1103/PhysRevLett.99.064101 )) was a method suited for general limit-cycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, and (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

Deliberative Policy Analysis

2018 ◽  
pp. 583-594
Author(s):  
Frank Fischer ◽  
Piyapong Boossabong
Keyword(s):  
Social Sciences ◽  
Decision Making ◽  
Policy Analysis ◽  
Policy Decision ◽  
Practical Method ◽  
Theoretical Perspectives ◽  
The Social ◽  
Policy Decision Making ◽  
Policy Problems

Deliberative policy analysis has its origins in the argumentative turn in policy analysis. It emerged as an alternative to the use of standard empirical-analytic methods of the social sciences to solve public policy problems. Not only has the conventional neopositivist approach failed to produce the promised results, it has generally operated with a technocratic, and largely an anti-democratic, bias. Basic to deliberative policy analysis is a method for bringing together a wider spectrum of citizens, politician and experts in the pursuit of policy decisions that are both effective and democratically legitimate. This chapter begins with an outline of the theoretical perspectives underlying deliberative policy analysis. Then, the process and practice is illustrated by the case study, which shows how the approach has moved from a theory to a practical method for policy decision-making.

scholarly journals A MODIFICATION OF AN ESTIMATION METHOD OF THE NATURAL FREQUENCY OF A CUBE FORM MICRO SATELLITE

2018 ◽  
Vol 6 (7) ◽  
pp. 121-131
Author(s):  
Kei-Ichi Okuyama ◽  
Shigeru Hibino ◽  
Misuzu Matsuoka ◽  
Sidi A. Bendoukha ◽  
Aleksander Lidtke
Keyword(s):  
Mechanical Property ◽  
Aluminum Alloy ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Estimation Method ◽  
Longitudinal Direction ◽  
Practical Method ◽  
Lateral Direction ◽  
Satellite Structure ◽  
Vibration Tests

Micro satellites must survive severe mechanical conditions during their launch phase. One design requirement for rockets is the stiffness requirement, i.e. the natural frequencies requirement. In the early stages of satellite development, presumption of the natural frequency of a satellite may be difficult. The material used for the structure of many micro satellites is an aluminum alloy. The structure subsystem occupies a large portion of the satellite mass, and the elastic modulus of this aluminum alloy is larger than that of other subsystems. Therefore, the mechanical property of the aluminum alloy cannot be used to represent the mechanical property of the whole satellite.  The density of an actual satellite differs from the density of the aluminum alloy.  Therefore, when estimating the minimum natural frequency, the size and the elastic modules of an actual satellite structure must be used. When using an actual satellite structure, the estimated minimum natural frequencies of the lateral direction and the longitudinal direction during the ascent phase are in agreement with the measured values acquired by the vibration tests. In order to shorten a process of satellite development, this paper describes a practical method for estimating the natural frequency of a cube-shaped micro satellite This paper is a modified version of the previous paper [1] using new measurement results.

scholarly journals AN ESTIMATION METHOD OF THE NATURAL FREQUENCY OF A CUBE FORM MICRO SATELLITE

2018 ◽  
Vol 6 (3) ◽  
pp. 88-97
Author(s):  
Kei-ichi OKUYAMA ◽  
Shigeru HIBINO ◽  
Misuzu MATSUOKA ◽  
Aleksander LIDTKE
Keyword(s):  
Mechanical Property ◽  
Aluminum Alloy ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Estimation Method ◽  
Longitudinal Direction ◽  
Practical Method ◽  
Lateral Direction ◽  
Satellite Structure ◽  
Vibration Tests

Micro satellites must survive severe mechanical conditions during their launch phase. One design requirement for rockets is the stiffness requirement, i.e. the natural frequencies requirement. In the early stages of satellite development, presumption of the natural frequency of a satellite may be difficult. The material used for the structure of many micro satellites is an aluminum alloy. The structure subsystem occupies a large portion of the satellite mass, and the elastic modulus of this aluminum alloy is larger than that of other subsystems. Therefore, the mechanical property of the aluminum alloy cannot be used to represent the mechanical property of the whole satellite.  The density of an actual satellite differs from the density of the aluminum alloy.  Therefore, when estimating the minimum natural frequency, the size and the elastic modules of an actual satellite structure must be used.  When using an actual satellite structure, the estimated minimum natural frequencies of the lateral direction and the longitudinal direction during the ascent phase are in agreement with the measured values acquired by the vibration tests. In order to shorten a process of satellite development, this paper describes a practical method for estimating the natural frequency of a micro satellite.

Guided Tuning of Turbine Blades: A Practical Method to Avoid Operating at Resonance

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Loc Duong ◽  
Kevin D. Murphy ◽  
Kazem Kazerounian
Keyword(s):  
Natural Frequencies ◽  
Turbine Blades ◽  
Practical Method ◽  
Laser Vibrometer ◽  
Operating Speed ◽  
Design Procedures ◽  
Iterative Design ◽  
At Resonance ◽  
Speed Range ◽  
Computationally Intensive

In gas turbine applications, forced vibrations of turbine blades under resonant—or nearly resonant—conditions are undesirable. Usually in airfoil design procedures, at least the first three blade modes are required to be free of excitation in the operating speed range. However, not uncommonly, a blade may experience resonance at other higher natural frequencies. In an attempt to avoid resonant oscillations, the structural frequencies are tuned away from the excitation frequencies by changing the geometry of the blade. The typical iterative design process—of adding and removing material through restacking the airfoil sections—is laborious and in no way assures an optimal design. In response to the need for an effective and fast methodology, the guided tuning of turbine blades method (GTTB) is developed and presented in this paper. A practical tuning technique, the GTTB method is based on structural perturbations to the mass and stiffness at critical locations, as determined by the methodology described herein. This shifts the excited natural frequency out of the operating speed range, while leaving the other structural frequencies largely undisturbed. The methodology is demonstrated here in the redesign of an actual turbine blade. The numerical results are experimentally validated using a laser vibrometer. The results indicate that the proposed method is not computationally intensive and renders effective results that jibe with experiments.

scholarly journals Synchronization transitions caused by time-varying coupling functions

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190275 ◽  
Author(s):  
Zeray Hagos ◽  
Tomislav Stankovski ◽  
Julian Newman ◽  
Tiago Pereira ◽  
Peter V. E. McClintock ◽  
...  
Keyword(s):  
Social Sciences ◽  
Dynamical Systems ◽  
Coupling Strength ◽  
Phase Synchronization ◽  
Time Variable ◽  
Time Variability ◽  
Time Varying ◽  
Theme Issue ◽  
Dynamical Interaction ◽  
Variable Coupling

Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying. Although much effort has been devoted to the analysis of coupling functions, the influence of time-variability on the associated dynamics remains largely unexplored. Motivated especially by coupling functions in biology, including the cardiorespiratory and neural delta-alpha coupling functions, this paper offers a contribution to the understanding of effects due to time-varying interactions. Through both numerics and mathematically rigorous theoretical consideration, we show that for time-variable coupling functions with time-independent net coupling strength, transitions into and out of phase- synchronization can occur, even though the frozen coupling functions determine phase-synchronization solely by virtue of their net coupling strength. Thus the information about interactions provided by the shape of coupling functions plays a greater role in determining behaviour when these coupling functions are time-variable. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

scholarly journals Recent advances in coupled oscillator theory

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190092 ◽  
Author(s):  
Bard Ermentrout ◽  
Youngmin Park ◽  
Dan Wilson
Keyword(s):  
Social Sciences ◽  
Coupled Oscillators ◽  
Weak Coupling ◽  
Standard Theory ◽  
Theme Issue ◽  
Coupled Oscillator ◽  
Dynamical Interaction ◽  
Weakly Coupled ◽  
The Stability ◽  
Oscillator Theory

We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems with applications to the Izhikevich neuron. We then introduce the idea of isostable reduction to explore behaviours that the weak coupling paradigm cannot explain. In an additional example, we show how bifurcations that change the stability of phase-locked solutions in a pair of identical coupled neurons can be understood using the notion of isostable reduction. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

scholarly journals Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190039 ◽  
Author(s):  
Tomislav Stankovski ◽  
Tiago Pereira ◽  
Peter V. E. McClintock ◽  
Aneta Stefanovska
Keyword(s):  
Social Sciences ◽  
Social Science ◽  
Respiratory Physiology ◽  
Theme Issue ◽  
Dynamical Interaction ◽  
Future Evolution ◽  
Interaction Mechanisms ◽  
Recent Developments ◽  
Functional Mechanisms ◽  
Breaking Work

Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions—which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

scholarly journals Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190045 ◽  
Author(s):  
M. Rosenblum ◽  
M. Frühwirth ◽  
M. Moser ◽  
A. Pikovsky
Keyword(s):  
Social Sciences ◽  
Heart Rate ◽  
Multivariate Data Analysis ◽  
Dynamics Model ◽  
Theme Issue ◽  
Sinus Arrhythmia ◽  
Dynamical Interaction ◽  
Phase Dynamics ◽  
Bivariate Data ◽  
Oscillatory Systems

We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

Analog Simulation of Phase Locked Modes of Diffusively Coupled van der Pol Oscillators

1999 ◽  
Author(s):  
Lesley Ann Low ◽  
Per G. Reinhall ◽  
Duane W. Storti
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Physical System ◽  
Coupled Oscillators ◽  
Electric Circuit ◽  
Van Der Pol ◽  
Analog Simulation ◽  
Coupling Parameters ◽  
Van Der Pol Oscillators ◽  
The Stability

Abstract Limit cycle oscillators arise in a wide variety of mechanical, electrical and biological systems. Recently, emphasis has been placed on the study of systems of coupled limit cycles, such as cardiac oscillations. Synchronization criteria have remained a focus of most investigations. One area of investigation in the field of coupled limit cycles is studying the behavior of a pair of linearly coupled van der Pol oscillators (Low, 1998; Rand, 1980; Sliger, 1997). Previous investigations (Storti, 1993; Storti, 1996) found the stability regions of the coupled oscillators for their in-phase and out-of-phase modes numerically. The coupled oscillators can be viewed as a mechanical system, where the coupling parameters are equivalent to a spring and damper attached between two masses. With positive coupling (positive damping) a region was found (Storti, 1993; Storti, 1996) where the in-phase mode is unstable. This counter intuitive result is yet to be discovered in a physical system of two coupled limit cycle oscillators. This research focuses on finding the region with positive coupling parameters where the in-phase mode is unstable using a physical model of two linearly coupled van der Pol oscillators. The coupled van der Pol oscillators were modeled using an analog electric circuit.

scholarly journals Characterization of real-world networks through quantum potentials

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254384
Author(s):  
Nicola Amoroso ◽  
Loredana Bellantuono ◽  
Saverio Pascazio ◽  
Alfonso Monaco ◽  
Roberto Bellotti
Keyword(s):  
Social Sciences ◽  
Real World ◽  
Network Connectivity ◽  
Small World ◽  
Formation Mechanisms ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network ◽  
Network Ensembles

Network connectivity has been thoroughly investigated in several domains, including physics, neuroscience, and social sciences. This work tackles the possibility of characterizing the topological properties of real-world networks from a quantum-inspired perspective. Starting from the normalized Laplacian of a network, we use a well-defined procedure, based on the dressing transformations, to derive a 1-dimensional Schrödinger-like equation characterized by the same eigenvalues. We investigate the shape and properties of the potential appearing in this equation in simulated small-world and scale-free network ensembles, using measures of fractality. Besides, we employ the proposed framework to compare real-world networks with the Erdős-Rényi, Watts-Strogatz and Barabási-Albert benchmark models. Reconstructed potentials allow to assess to which extent real-world networks approach these models, providing further insight on their formation mechanisms and connectivity properties.

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