scholarly journals Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis

Entropy ◽  
2018 ◽  
Vol 20 (1) ◽  
pp. 40 ◽  
Author(s):  
Max Trostel ◽  
Moses Misplon ◽  
Andrés Aragoneses ◽  
Arjendu Pattanayak
Keyword(s):  
Complex Dynamics ◽  
Duffing Oscillator ◽  
Ordinal Patterns

An Information Theoretic Study of a Duffing Oscillator Array Reservoir Computer

2021 ◽  
Author(s):  
Md Raf E Ul Shougat ◽  
XiaoFu Li ◽  
Tushar Mollik ◽  
Edmon Perkins
Keyword(s):  
Information Theory ◽  
Complex Dynamics ◽  
Duffing Oscillator ◽  
Temporal Data ◽  
Information Theoretic ◽  
Oscillatory Systems ◽  
Processing Ability ◽  
Information Metric ◽  
Immense Potential ◽  
Insight Into

Abstract Typically, nonlinearity is considered to be problematic and sometimes can lead to dire consequences. However, the nonlinearity in a Duffing oscillator array can enhance its ability to be used as a reservoir computer. Machine learning and artificial neural networks, inspired from the biological computing framework, have shown their immense potential, especially in real-time temporal data processing. Here, the efficacy of a Duffing oscillator array is explored as a reservoir computer by using information theory. To do this, a reservoir computer model is studied numerically, which exploits the dynamics of the array. In this system, the complex dynamics stem from the Duffing term in each of the identical oscillators. The effects of various system parameters of the array on the information processing ability is discussed from the perspective of information theory. By varying these parameters, the information metric was found to be topologically mixed. Additionally, the importance of asynchrony in the oscillator array is also discussed in terms of the information metric. Since such nonlinear oscillators are used to model many different physical systems, this research provides insight into how physical nonlinear oscillatory systems can be used for dynamic computation, without significantly modifying or controlling the underlying dynamical system. To the authors' knowledge, this is the first use of Shannon's information rate for quantifying a reservoir computer of this kind, as well as the first comparison between synchronization phenomena and the computing ability of a reservoir.

Modeling Nonlinear MEMS Beams and the Chaotic Duffing Oscillator in SPICE

2017 ◽  
Vol 2017 (DPC) ◽  
pp. 1-90
Author(s):  
Aubrey Nathan Beal
Keyword(s):  
Young’S Modulus ◽  
Complex Dynamics ◽  
Nonlinear Oscillations ◽  
Young's Modulus ◽  
Circuit Simulation ◽  
Duffing Oscillator ◽  
Single Crystal Silicon ◽  
Mems Devices ◽  
Crystal Silicon ◽  
Cross Sectional

Nonlinear MEMS beams have been modeled using SPICE. This allows for the complex dynamics of MEMS resonators to be observed parallel to their supporting electronics via circuit simulation. Silicon generally provides suitably linear parameters for use in MEMS. However, nonlinearities may arise due to issues such as amplitude-frequency (A-F) effect, large displacement of the proof mass, pull-in voltage, fatigue, material or electrical parameters, process variation, simplified beam modeling and nonlinear spring constants. By modeling these effects in SPICE, the design of electronics that automatically test, calibrate, report or even mitigate these effects is aided. Single-crystal silicon is a highly linear material up until its failure, especially type <100>. High quality factor MEMS devices may, however, be affected by even small nonlinear terms in the material's Young's modulus. Geometric deformations may also occur due to decreases in cross-sectional area of beams in reaction to stretching and loading. Specifically, by including nonlinear geometric effects of MEMS beams and nonlinear terms in the Young's modulus of <100> and <110> silicon - nonlinear and chaotic oscillations are shown to arise via SPICE simulation. Using this SPICE modeling method, electronic systems were designed to monitor the nonlinear parameters of MEMS beams that cause A-F effect and chaotic Duffing oscillations. Extracting parameters such as those from the oscillation's Poincare section may yield advantage in built-in self-test (BIST) applications. The features in these nonlinear oscillations extend parameters to monitor and potentially calibrate MEMS devices for reliability, stability and processing variation.

scholarly journals Ordinal patterns in the Duffing oscillator: Analyzing powers of characterization

2021 ◽  
Vol 31 (2) ◽  
pp. 023104
Author(s):  
Ivan Gunther ◽  
Arjendu K. Pattanayak ◽  
Andrés Aragoneses
Keyword(s):  
Duffing Oscillator ◽  
Analyzing Powers ◽  
Ordinal Patterns

Frontiers in Complex Dynamics

2014 ◽  
Author(s):  
Araceli Bonifant ◽  
Misha Lyubich ◽  
Scott Sutherland
Keyword(s):  
Historical Perspective ◽  
Complex Dynamics ◽  
Short Paper ◽  
Combinatorial Group Theory ◽  
Entropy Theory ◽  
Holomorphic Dynamics ◽  
Eightieth Birthday ◽  
Several Variables ◽  
Fields Medal ◽  
Combinatorial Group

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

An Alternative Approach To User Fee Policy In The Primary Health Care Setting Of Bangladesh.

2020 ◽  
Author(s):  
Nazneen Akhter
Keyword(s):  
Health Care ◽  
Primary Health Care ◽  
Complex Dynamics ◽  
Quality Care ◽  
Secondary Data ◽  
User Fees ◽  
Primary Health ◽  
Alternative Approach ◽  
Benefit Principle ◽  
User Fee

The concept of ascribing user fee in health care settings always remained a policy struggle and countries experienced different learning in this regards while implementing user fee at different tiers of health settings. The most exquisite learning among the many country specific evidences related to user fee are the match and mismatch between the equity principle and benefit principle while considering the client perspective. There is an added dimension of quality care which also add more complex dynamics into this concept since the quality care consideration has a double edged perspective both for clients and providers, where which one will get superiority over whom is a great question in health care, especially in the Primary Health care (PHC) of the country. In this reality the appropriate implementation guideline, followed by an appropriate practice of the administrative and management both service oriented and financial are of great importance in this user fee implementation consideration which always remained a challenge in the health care specially in remote care of PHC. This paper attempted a secondary data searching and scoping the available documents of Bangladesh and across the world to find an alternative approach to user fees policy where equity and benefit principle and quality - these three have to be placed in a well-constructed triad in PHC implementation which has been recommended as an alternative policy imperative in approaching user fees for Bangladesh PHC settings.

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