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International Conference on Fractional Differentiation and Its Applications (ICFDA)

作者： Iqbal M. Batiha Noureddine Djenina Adel Ouannas Taki-Eddine Oussaeif Leila Ben Aoua Shaher Momani Department of Mathematics Al Zaytoonah University of Jordan Amman Jordan Nonlinear Dynamics Research Center (NDRC) Ajman University Ajman UAE Laboratory of Dynamical Systems and Control University of Larbi Ben M’hidi Oum El Bouaghi Algeria Department of Mathematics and Computer Science University of Oum EL-Bouaghi Oum El Bouaghi Algeria Department of Mathematics and Computer Science University of Larbi Ben M’hidi Oum El Bouaghi Algeria

The mathematical study of the growth of a cancer tumor gives us great progress in knowing the behavior of the cancer tumor as well as taking appropriate therapeutic measures. In this article, we endeavor to investigate a mathematical model of a cancer tumor and study its stabilization. In particular, we first discritize the continuous model connected with the dynamics of cancer tumor to get the discrete model. Then we perform several numerical simulations that will show that the proposed discrete model can behave chaotically. As a result, we study the unique fixed point stability that has a physical meaning, and finally we controlled the proposed system to stabilized its dynamics at such a point.

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A Parametric Study of an Electrothermal Oscillator Based on Shape Memory Alloys

A Parametric Study of an Electrothermal Oscillator Based on ...

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International Symposium on Electrical Apparatus and Technologies (SIELA)

作者： Todor Todorov Rosen Mitrev Ivan Yatchev Andrei Fursov Alexander Ilin Vasily Fomichev Department of Theory of Mechanisms and Machines Technical University of Sofia Sofia Bulgaria Department of Logistics Engineering Technical University of Sofia Sofia Bulgaria Department of Ellectrical Apparatus Technical University of Sofia Sofia Bulgaria Department of Nonlinear Dynamical Systems and Control Processes Lomonosov Moscow State University Moscow Russia

ISBN: (数字)9781728143460

ISBN: (纸本)9781728143477

The paper presents a parametric study of an electrothermal oscillator based on Shape Memory Alloy. The operating principle of the oscillator is established on a heated by electric current Shape Memory Alloy wire, mounted with a pre-tension between the free ends of two symmetrically placed cantilever beams. The effect of crystallographic changes in the wire due to heating leads to the generation of mechanical and electrical vibrations. Parametric studies were conducted to investigate the influence of the input parameters on the system output characteristics.

关键词： Wires Oscillators Shape memory alloys Electrodes Vibrations Mathematical model Parametric study

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Fractional-order biological system: chaos, multistability and coexisting attractors

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The European Physical Journal Special Topics 2021年第5期231卷 1061-1070页

作者： Debbouche, Nadjette Ouannas, Adel Momani, Shaher Cafagna, Donato Pham, Viet-Thanh Laboratory of Dynamical System and Control University of Larbi Ben M’hidi Oum El Bouaghi Algeria Department of Mathematics and Computer Sciences Larbi Ben M’hidi University Oum El Bouaghi Algeria Nonlinear Dynamics Research Center (NDRC) College of Humanities and Sciences Ajman University Ajman UAE Department of Mathematics Faculty of Science University of Jordan Amman Jordan Department of Innovation Engineering University of Salento Lecce Italy Nonlinear Systems and Applications Faculty of Electrical and Electronics Engineering Ton Duc Thang University Ho Chi Minh City Vietnam

In this paper, the nonlinear dynamics of the biological system modeled by the fractional incommensurate order Van der Pol equations are investigated. The stability of the proposed fractional non-autonomous system is analyzed by varying both the fractional order derivative and system parameters. Moreover, very interesting phenomena such as symmetry, multi-stability and coexistence of attractors are discovered in the considered biological system. Numerical simulations are performed by considering the Caputo fractional derivative and results are reported by means of bifurcation diagrams, computation of the largest Lyapunov exponent, phase portraits in 2D and 3D projections.

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Modeling and study of a novel electrothermal oscillator based on shape memory alloys

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IOP Conference Series: Materials Science and Engineering 2020年第1期878卷

作者： R P Mitrev E I Atamas O I Goncharov T S Todorov I I Iatcheva Department of Logistics Engineering Technical University of Sofia Sofia 1000 Bulgaria Department of Nonlinear Dynamical Systems and Control Processes Lomonosov Moscow State University Moscow Russia Department of Theory of Mechanisms and Machines Technical University of Sofia Sofia 1000 Bulgaria Department of Theoretical Electrical Engineering Technical University of Sofia Sofia 1000 Bulgaria

The paper deals with mathematical modelling and experimental investigation of a novel electrothermal oscillator based on Shape Memory Alloys (SMA). The operation of the oscillator is based on a heated by DC electric current SMA wire, mounted with a pre-tension between the free ends of two symmetrically arranged cantilever beams. Crystallographic changes in the SMA wire, consisting in the transition between austenitic and martensitic phases due to the periodic heating and cooling, lead to its intermittent shortening and stretching and thus mechanical and electrical vibrations are generated. The mathematical model of the system is derived using Lagrange-Maxwell formalism, Joule–Lenz law and Newton's law of cooling. Simulation results show two types of periodic motion – the first one with low frequency is due to the temperature variation in the wire and the second one is with much more higher frequency and is due to the mass and elastic properties of the system. Experimental validation of the mathematical model shows its suitability for description of the considered system dynamic behaviour.

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A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfaces 2nd

A brief survey on singularities of geodesic flows in smooth ...

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2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015

作者： Pavlova, N.G. Remizov, A.O. Department of Nonlinear Analysis and Optimization RUDN University Moscow Russia V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences Moscow Russia Laboratory of Dynamical Systems National Research University Higher School of Economics Moscow Russia

ISBN: (纸本)9783319736389

We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold S changes its signature (degenerates) along a curve S0, which locally separates S into a Riemannian (R) and a Lorentzian (L) domain. The geodesic flow does not have singularities over R and L, and for any point q∈ R∪ L and every tangential direction p∈ there exists a unique geodesic passing through the point q with the direction p. On the contrary, geodesics cannot pass through a point q∈ S0 in arbitrary tangential directions, but only in some admissible directions;the number of admissible directions is 1 or 2 or 3. We study this phenomenon and the local properties of geodesics near q∈ S0. © Springer International Publishing AG, part of Springer Nature 2018.

关键词： Surveys

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The Peregrine breather on the zero-background limit as the two-Soliton degenerate solution: An experimental study

arXiv

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arXiv 2020年

作者： Chabchoub, Amin Slunyaev, Alexey Hoffmann, Norbert Dias, Frédéric Kibler, Bertrand Genty, Goëry Dudley, John M. Akhmediev, Nail Centre for Wind Waves and Water School of Civil Engineering University of Sydney SydneyNSW2006 Australia Marine Studies Institute University of Sydney SydneyNSW2006 Australia Department of Nonlinear Geophysical Processes Institute of Applied Physics RAS Nizhny Novgorod Russia Laboratory of Dynamical Systems and Applications National Research University Higher School of Economics Nizhny Novgorod Russia Dynamics Group Hamburg University of Technology Hamburg21073 Germany Department of Mechanical Engineering Imperial College London LondonSW7 2AZ United Kingdom School of Mathematics and Statistics University College Dublin Dublin Ireland Université Paris-Saclay ENS Paris-Saclay CNRS Centre Borelli Gif-sur-Yvette91190 France UMR 6303 CNRS-Université Bourgogne Franche-Comté Dijon21078 France Photonics Laboratory Physics Unit Tampere University Tampere33014 Finland Institut FEMTO-ST Université Bourgogne Franche-Comté CNRS UMR 6174 Besançon France Department of Theoretical Physics Research School of Physics Australian National University CanberraACT2600 Australia

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics. © 2020, CC-BY.

关键词： Solitons

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Sparse and Optimal Wide-Area Damping control in Power Networks

Sparse and Optimal Wide-Area Damping Control in Power Networ...

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American control Conference

作者： Florian Dorfler Mihailo R. Jovanovic Michael Chertkov Francesco Bullo Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106 Department of Electrical and Computer Engineering University of Minnesota Minneapolis MN 55455 Theory Division & Center for Nonlinear Studies at LANL and with New Mexico Consortium Los Alamos NM 87544

ISBN: (纸本)9781479901777

Inter-area oscillations in power networks are typically poorly controllable by means of local decentralized control. Recent research efforts have been aimed at developing wide-area control strategies that involve communication of remote signals. In conventional wide-area control strategies the control structure is fixed a priori typically based on modal criteria. In contrast, here we employ the recently introduced paradigm of sparsity-promoting optimal control to simultaneously identify the control structure and optimize the closed-loop performance. To induce a sparse control architecture, we regularize the standard quadratic performance index with an l_1-penalty on the feedback matrix. The quadratic objective functions are inspired by the classic slow coherency theory and are aimed at imitating homogeneous networks without interarea oscillations. We use a compelling example to demonstrate that the proposed combination of the sparsity-promoting optimal control design with the slow coherency objective functions performs almost as well as the optimal centralized controllers.

关键词： Power grids control Architecture damped control design control Objective function Optimal control quadratic performance index homogeneous network

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Robot Swarming over the Internet

Robot Swarming over the Internet

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American control Conference

作者： Jerome Gilles Balaji R. Sharma Will Ferenc Hannah Kastein Lauren Lieu Ryan Wilson Yuan Rick Huang Andrea L. Bertozzi Baisravan HomChaudhuri Subramanian Ramakrishnan Manish Kumar Department of Mathematics University of California Los Angeles 520 Portola Plaza Los Angeles CA 90095-1555 U.S.A. School of Dynamical Systems 629 Rhodes Hall University of Cincinnati Cincinnati OH 45221 U.S.A. Department of Engineering Harvey Mudd College 301 Platt Boulevard Claremont CA 91711 U.S.A. Anteros Labs Inc Torrance CA 90505 U.S.A. Center for Nonlinear Dynamics and Control Villanova University Villanova PA 19085 U.S.A.

ISBN: (纸本)9781457710957

We consider cooperative control of robots involving two different testbed systems in remote locations in different time zones, with communication on the internet. The goal is to have all robots properly follow a leader defined on one of the testbeds, while maintaining non-overlapping positions within each swarm and between swarms, assuming they are superimposed in the same virtual space. A dual-testbed design is developed involving real robots and remote network communication, performing a cooperative swarming algorithm based on a modified Morse Potential. Extensive experimental results were obtained with real internet communication and virtual testbeds running in each lab. The communication protocol was designed to minimize loss of packets, and average transfer delays are within tolerance limits for practical applications. We ran several experiments, with intentional packet loss, that illustrate the degradation of the results in the case of modest and severe packet loss. The novelty of this work is its experimental aspect involving long range network communication across a large distance via the internet. The work raises a series of interesting theoretical problems.

关键词： Internets Robot Packet loss Communication protocols Swarming coordinated control Network communication Remote locations swarms dike swarms Packet Communication Research Internet-based communication

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Announcements, comments, and acknowledgments

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AIAA Journal 2006年第1期44卷 1-10页

作者： Oran, Elaine Kailasanath, Kazhikathra Aggarwal, Suresh K. Ahmadian, Mehdi Alexandrov, Natalia Auweter-Kurtz, Monika Bailly, Christophe Balachandran, Balakumar Berman, Alex Candler, Graham V. Chelliah, Harsha K. Chokani, Ndaona Fujii, Kozo Gaitonde, Datta V. Ghia, Kirti Karman N. Givi, Peyman Gore, Jay P. Kaplan, Carolyn R. Livne, Eli Lucht, Robert P. Messac, Achille Wing, N.G. Palazotto, Anthony N. Pierre, Christophe Plotkin, Allen Roy, Ajit K. Saigal, Sunil Sforza, Pasquale M. Shivakumar, Kunigal N. So, Ronald M.C. Springer, Anthony M. Anatolitumin, Anthony M. Zhong, Xiaolin United States Division of Computational Physics United States United States AIAA United States APS United States National Academy of Engineering United States Center for Reactive Flow and Dynamical Systems Naval Research Laboratory United States Institute of Physics Department of Mechanical Engineering University of Illinois at Chicago United States ASME Combustion Institute Department of Mechanical Engineering Virginia Polytechnic Institute State University United States Aeronautics Systems Analysis Branch NASA Langley Research Center United States SIAM ISSMO Aerospace Engineering Institute of Space Systems Universität Stuttgart Germany Amelia Earhart Italy International Amelia Earhart Award Committee Italy France France Mechanical Engineering University of Maryland College Park United States AAM SPIE ASA ASME Technical Committees of Multi-Body Systems Nonlinear Dynamics Dynamics and Control of Structures and Systems American Helicopter Society United States Aerospace Engineering and Mechanics University of Minnesota United States AIAA Thermophysics Technical Committee Mechanical and Aerospace Engineering University of Virginia United States AIAA Propellants and Combustion Technical Committee AIAA's Transition Study Group Aerodynamics Measurement Technology Technical Committee Thermophysics Technical Committee Japan MOSAIC project on the Technology Pressure-sensitive Paint Measurement System Japan High-Speed Flows Group Air Vehicles Directorate Air Force Research Laboratory Wright-Patterson Air Force Base United States Wright State University United States Aerospace Engineering and Engineering Mechanics United States United States Mechanical Engineering University of Pittsburgh United States School of Mechanical Engineering Purdue University United States Committee on Heat Transfer in Fire and Combustion Systems Japan Board of Advisors Central States Section Combustion Institute United States AIChE United States Tau Beta Pi United States

No abstract available

关键词： Institute of Space and Astronautical Science American Society of Mechanical Engineers Direct Numerical Simulation Aerospace Engineering MDO Propellant Air Forces Aerodynamics Heterogeneous Combustion NASA Langley Research Center

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Statistical Theory of Asteroid Escape Rates

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Physical Review Letters 2002年第1期89卷 011101-011101页

作者： Charles Jaffé Shane D. Ross Martin W. Lo Jerrold Marsden David Farrelly T. Uzer Control and Dynamical Systems Division 107-81 California Institute of Technology Pasadena California 91125 Navigation and Flight Mechanics Jet Propulsion Laboratory Pasadena California 91109-8099 Department of Chemistry West Virginia University Morgantown West Virginia 26506-6045 Department of Chemistry Utah State University Logan Utah 84322-0300 Center for Nonlinear Sciences and School of Physics Georgia Institute of Technology Atlanta Georgia 30332-0430

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations.

关键词： .numerical simulations rates chemical reaction transition states mass transport orbits chaotic phase space escape celestial mechanics comets Farrelly Uzer circumplanetary Solar System

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