Recent Advances In Applied Nonlinear Dynamics With Numerical Analysis
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| Author | : Changpin Li |
| Publisher | : World Scientific |
| Total Pages | : 414 |
| Release | : 2013 |
| Genre | : Science |
| ISBN | : 9814436461 |
Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation.Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed.In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc.In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications.
| Author | : Ali H. Nayfeh |
| Publisher | : John Wiley & Sons |
| Total Pages | : 700 |
| Release | : 2008-11-20 |
| Genre | : Science |
| ISBN | : 3527617558 |
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
| Author | : Jan Awrejcewicz |
| Publisher | : World Scientific |
| Total Pages | : 561 |
| Release | : 2021-07-26 |
| Genre | : Science |
| ISBN | : 981122191X |
In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.
| Author | : Bram De Kraker |
| Publisher | : World Scientific |
| Total Pages | : 462 |
| Release | : 2000-04-28 |
| Genre | : Technology & Engineering |
| ISBN | : 9814497908 |
Rapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes.The main objective of this volume is to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos.The main focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials and dynamics of metal cutting.
| Author | : Daniel Kaplan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 438 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461208238 |
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.
| Author | : M. Vidyasagar |
| Publisher | : SIAM |
| Total Pages | : 515 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898719185 |
When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.
| Author | : Walter Lacarbonara |
| Publisher | : Springer Nature |
| Total Pages | : 350 |
| Release | : 2020-01-27 |
| Genre | : Science |
| ISBN | : 3030347249 |
This third of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to New Trends in Nonlinear Dynamics. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume III include NEMS/MEMS and nanomaterials: multi-sensors, actuators exploiting nonlinear working principles; adaptive, multifunctional, and meta material structures; nanocomposite structures (e.g., carbon nanotube/polymer composites, composites with functionalized nanoparticles); 0D,1D,2D,3D nanostructures; biomechanics applications, DNA modeling, walking dynamics, heart dynamics, neurodynamics, capsule robots, jellyfish-like robots, nanorobots; cryptography based on chaotic maps; ecosystem dynamics, social media dynamics (user behavior dynamics in multi-messages social hotspots, prediction models), financial engineering, complexity in engineering; and network dynamics (multi-agent systems, leader-follower dynamics, swarm dynamics, biological networks dynamics).
| Author | : Gerasimos Rigatos |
| Publisher | : Cambridge Scholars Publishing |
| Total Pages | : 741 |
| Release | : 2020-11-19 |
| Genre | : Technology & Engineering |
| ISBN | : 1527562468 |
This volume discusses advances in applied nonlinear optimal control, comprising both theoretical analysis of the developed control methods and case studies about their use in robotics, mechatronics, electric power generation, power electronics, micro-electronics, biological systems, biomedical systems, financial systems and industrial production processes. The advantages of the nonlinear optimal control approaches which are developed here are that, by applying approximate linearization of the controlled systems’ state-space description, one can avoid the elaborated state variables transformations (diffeomorphisms) which are required by global linearization-based control methods. The book also applies the control input directly to the power unit of the controlled systems and not on an equivalent linearized description, thus avoiding the inverse transformations met in global linearization-based control methods and the potential appearance of singularity problems. The method adopted here also retains the known advantages of optimal control, that is, the best trade-off between accurate tracking of reference setpoints and moderate variations of the control inputs. The book’s findings on nonlinear optimal control are a substantial contribution to the areas of nonlinear control and complex dynamical systems, and will find use in several research and engineering disciplines and in practical applications.
| Author | : Andreas Galka |
| Publisher | : World Scientific |
| Total Pages | : 360 |
| Release | : 2000-02-18 |
| Genre | : Science |
| ISBN | : 9814493929 |
This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of the underlying dynamics, as introduced by nonlinear dynamics. In particular, current algorithms for state space reconstruction, correlation dimension estimation, testing for determinism and surrogate data testing are presented — algorithms which have been playing a central role in the investigation of deterministic chaos and related phenomena since 1980. Special emphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram.
| Author | : Walter Lacarbonara |
| Publisher | : Springer Nature |
| Total Pages | : 570 |
| Release | : 2020-01-29 |
| Genre | : Science |
| ISBN | : 3030347133 |
This first of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics of Structures, Systems and Devices. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume I include multi-scale dynamics: coexistence of multiple time/space scales, large system dynamics; dynamics of structures/industrial machines/equipment/facilities (e.g., cable transportation systems, suspension bridges, cranes, vehicles); nonlinear interactions: parametric vibrations with single/multi-frequency excitations, multiple external and autoparametric resonances in multi-dof systems; nonlinear system identification: parametric/nonparametric identification, data-driven identification; experimental dynamics: benchmark experiments, experimental methods, instrumentation techniques, measurements in harsh environments, experimental validation of nonlinear models; wave propagation, solitons, kinks, breathers; solution methods for pdes: Lie groups, Hirota’s method, perturbation methods, etc; nonlinear waves in media (granular materials, porous materials, materials with memory); composite structures: multi-layer, functionally graded, thermal loading; fluid/structure interaction; nonsmooth and retarded dynamics: systems with impacts, free play, stick-slip, friction hysteresis; nonlinear systems with time and/or space delays; stability of delay differential equations, differential-algebraic equations; space/time reduced-order modeling: enhanced discretization methods, center manifold reduction, nonlinear normal modes, normal forms; fractional-order systems; computational techniques: efficient algorithms, use of symbolic manipulators, integration of symbolic manipulation and numerical methods, use of parallel processors; and multibody dynamics: rigid and flexible multibody system dynamics, impact and contact mechanics, tire modeling, railroad vehicle dynamics, computational multibody dynamics.
