Handbook of Applications of Chaos Theory ( 1100 Pages)
Last updated: 14 March 2013
Handbook of Applications of Chaos Theory (~1100 pages)
Table of Contents (tentative, may include more or less topics and chapters)
Colour marks indicate the proposed topics by the authors.
Please inform us if you select from the non-coloured topics to add and include in your submission if appropriate.
1. Introduction1.A. Chaos and Nonlinear Dynamics (60 pages)
Nonlinear dynamics of continuous, discontinuous and hybrid systems / Bogdan Epureanu, Dept of Mech Engineering
University of Michigan, Ann Arbor, MI, USA
Nonlinear dynamics and chaos in engineering applications
System Augmentation for Sensing: Theory and Applications
Qualitative and quantitative analysis of nonlinear dynamic systems
Complex dynamical systems
Classical Deterministic Chaos
Numerical and geometrical methods in nonlinear dynamics
1.B. Dynamical processes: theory and applications (50 pages)
Differential equations and new transforms applications / A.G. Ramm, Kansas State University
Kansas, USA
Valerio Lucarini, Meteorological Institute
University of Hamburg, Germany
Nonlinear fractional partial differential equations
Large-time behavior of solutions to nonlinear evolution equations
Integral equations and applications
Topological dynamics
Asymptotic Methods
Chaotic network dynamics
Response theory and Lyapunov exponents
Lyapunov covariant vectors
1.C. Computational Aspects (50-80 pages)
Computer aided symbolic methods in dynamics / Bogdan Epureanu, Univ of Michigan, Ann Arbor, MI, USA
Paul Meehan,Mechanical and Mining Eng
The University of Queensland, Australia
Gennady A. Leonov-Nikolay Kuznetsov
Saint-Petersburg State University, Russia
Shijun Liao
State Key Lab of Ocean Engineering
Dept. of Mathematics
Shanghai Jiao Tong University
Shanghai, China
Symmetries and perturbation methods
Quantifying Attractor Morphing by Sensitivity Vector Fields
Applications of chaos in mechanics: across spacecraft, mining, trains and brains
Numerical visualization of attractors:
self-exciting and hidden attractors
Evolutionary computation to chaotic Systems
The clean numerical simulations of chaos and its application
Numerical Simulations
Applications
1.D. Chaos: critical behavior and universality (50 pages)
Phase diagrams / Avadis Hacinliyan
Department of Physics, Yeditepe University, Kayisdagi, Istanbul, Turkey
Gennady A. Leonov-Nikolay Kuznetsov
Saint-Petersburg State University, Russia
Bifurcation theory
Analysis of bifurcations and chaos
Hopf Bifurcation, sequence of period-doubling bifurcations and chaos
Chaotic models and attractors (Logistic, Hénon, Lorenz, Rössler,...)
Lyapunov functions
1. E. Fractals (50 pages)
Fractals and self-similarity (The Cantor set, the Sierpinski carpet,…) / V. P. Drakopoulos
Department of Informatics & Telecommunications
University of Athens
Athens, Greece
Fractals and the problem of dimension
Julia sets and Mandelbrot sets
Growing fractals, images and shapes
Fractal curves, functions and images: An iterated journey to complex dynamics through compression and interpolation
1.F. Synchronization and control of dynamical systems (60 pages)
Identical synchronization
Stability and Bifurcations of Synchronized, Mutually Coupled Chaotic Systems
Stability for Coupled, Chaotic Systems
Synchronizing with Functions of the Dynamical Variables
1.G. Chaos in the Driven Damped Oscillators (60 pages)
Chaos in the Forced Damped Oscillators with Analytical Nonlinearities / Mikhail V. Zakrzhevsky
Institute of Mechanics,
Riga Technical University, Riga, Latvia
Chaos in the Forced Damped Piece-wise Linear Oscillators
Dynamical Chaos in the Forced Damped Pendulum Oscillators
1.H. Limited Power Supply Non-ideal Systems and Deterministic Chaos (60 pages)
Systems with limited power-supply (non-ideal systems as manifestations of Sommerfeld – Kononenko effect) and applications Numerical techniques of investigation of deterministic chaos in non-ideal systems.
Non-ideality as main reason of origination of chaos
Peculiarities of chaotic behaviour of some non-ideal systems (pendulum systems, electroelastic systems, low-dimensional hydromechanics systems) / Aleksandr Yu. Shvets
National Technical University of Ukraine "Kyiv Polytechnic Institute
Kyiv, Ukraine
2. Stochastic Chaos (40 pages)
Stochastic Chaos versus Deterministic / Christos H Skiadas, Technical University of Crete, Chania, Crete, Greece
Bifurcation to stochastic chaos
Stochastic global bifurcation in perturbed Hamiltonian systems
Stochastic chaos in Fokker-Planck equations
Stochastic chaos and its control
Bifurcation and Chaotic Analysis of Stochastic Duffing System
Stochastic chaos: an analogue of quantum chaos
Heterogeneity and stochastic chaos in stock markets
Stochastic chaos in Ecology
The transition from deterministic chaos to a stochastic process
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems
Stochasticity and deterministic chaos
Nonlinear Stochastic Systems
3. Spatiotemporal Chaos (60-80 pages)
Reaction diffusion patterns / Paul Manneville
LadHyX, Hydrodynamics Laboratory, CNRS UMR7646, École Polytechnique - Palaiseau, France
Rayleigh-Bénard convection
Von Karman vortex streets
Nonlinear pattern dynamics and the Ginzburg-Landau formalism
Spatiotemporal intermittency
Phase instabilities and phase turbulence (the Kuramoto-Sivashinsky equation)
Chemical reaction chaos -Belousov-Zhabotinsky reactions
4. Data Analysis and Chaos (50 pages)
Analysis of chaotic data / Avadis Hacinliyan
Department of Physics, Yeditepe University, Kayisdagi, Istanbul, Turkey
Alexander V. Glushkov
Odessa State University-OSENU, Odessa, Ukraine
Chaos and time-series analysis
Principal Component Analysis and Chaos
Chaos Theory Methods in Nonlinear Forecasting of Dynamical Systems Evolution
Chaos and innovation
Polynomial chaos
Embedding chaos
5. Hydrodynamics and Turbulence (50 pages)
Turbulence / Diego Angeli
DIEF - Dipartimento di Ingegneria "Enzo Ferrari", Università degli Studi di Modena e Reggio Emilia, Modena, Italy
Turbulent Transport and Simulation
Reliable numerical modelling of complex dynamics in confined thermal flows
Entropy of particles on a turbulent sea
Fluid Mechanics and Turbulence
Chaotic advection
Chaotic advection in oscillatory flows
6. Optics and Chaos (30 pages)
Nonlinear optics / Vladimir L. Kalashnikov,
Institut für Photonik, TU Wien,
Wien Austria
The optical rogue waves
Laser optics and chaos
The Ikeda attractor
Quantum chaos
7. Chaotic Oscillations and Circuits (60-80 pages)
Chaotic delay equations / Leszek Sirko
Institute of Physics, Polish Academy of Sciences, Warszawa, Poland
Gennady A. Leonov- Nikolay Kuznetsov
Saint-Petersburg State University, Russia
Banlue Srisuchinwong
Sirindhorn Int Institute of Technology , (SIIT)
Bangkadi Thammasat University,Thailand
Chaotic communication
Chaotic oscillators
Phenomena and criteria of chaotic oscillations
Isoscattering microwave networks
Nonlinear Vibrations and Applications
Van der Pol oscillators
Chaotic synchronization
SHILNIKOV Chaos
CHUA’S oscillators
Synchronization and delay between signals
Nonlinear filtering and communication
Chaotic Circuits Based on a Diode
Chaos and multi channel communication
8. Chaos in Climate Dynamics (30 pages)
Chaos in simplified Climate Models (The Lorenz model)
Weather forecasts
Earth's climate
9. Geophysical Flows (40 pages)
Geodesic flows / S.V. Prants
Pacific Oceanological Institute of the Russian Academy of Sciences,
Vladivostok, Russia
Spatially extended systems
Chaotic mixing in the ocean
Nonlinear dynamics of ocean flows
Spatiotemporal pattern formation and chaos
Vortex ripples in sand
Coupled map lattice and spatiotemporal pattern formation
Self-Organized criticality
Multifractal geophysics
10. Biology and Chaos (30 pages)
Computational Biology and Chaos
Fractal geometry in Biology
Chaos control in Biology
Nonlinear dynamics of protein folding
Biomechanics
11. Neurophysiology and Chaos (30 pages)
Neurons and Chaos
Chaos in the Brain
Chaos in the Heart
Neurocomputation
Parameter estimation for neuron models
12. Quantum chaos and Hamiltonian Systems (40 pages)
Chaotic interference versus decoherence: external
noise, state mixing and quantum-classical
correspondence / Valentin V. Sokolov
Budker Institute of Nuclear Physics
Theory Department
Novosibirsk, Russia
Flow equations for Hamiltonians
Hamiltonian and Quantum Chaos
13. Chaos in Astronomy and Astrophysics (50-70 pages)
Chaos in the Solar system / Alexander Kholtygin
Astronomical Institute, Saint-Petersburg University, Saint-Petersburg, Russia
N. Jevtic
Bloomsburg University, Bloomsburg, PA, USA
N-body Chaos
Dynamics and Optimization of Multibody Systems
Chaos in Galaxies
The Hénon-Heiles system
Order and chaos in galaxies
Galaxy simulations
Applications of Chaos Theory: Nonlinear Time Series Analysis of Kepler Space Telescope Variable-Star Data
14. Chaos in Plasma Physics (50 pages)
Dynamics of plasmas and chaos / Dan-Gheorghe Dimitriu
Faculty of Physics
“Alexandru Ioan Cuza” University of Iasi, Romania
Complex space charge structures in plasma
Oscillations and instabilities in plasma
Laser ablation plasma
15. Chaos and Solitons (40 pages)
Integrable Systems and Solitons
The Korteweg de Vries equation
Bifurcation and chaos in the generalized Korteweg-de Vries equation
The generalized KdV-Burgers' equation
The Zakharov-Kuznetsov equation
The sine-Gordon equation
The generalized Burgers-Huxley equation
Darboux transformations for soliton equations
16. Micro- and Nano- Electro-Mechanical Systems (30-50 pages)
Electrospun Nanofibers and applications / D. Laroze
Max Planck Institute for Polymer Research, Mainz, Germany
Nonlinear phenomena in electrospinning
Complex Dynamics of parametrically driven magnetic systems
Micro egg-shaped product via electrospinning
17. Neural Networks (50 pages)
Discrete-time recurrent neural networks / John Oommen
School of Computer Science, Carleton University
Ottawa, ON, Canada
THE SCIENCE AND ART OF CHAOTIC PATTERN RECOGNITION
Delayed neural networks
Fuzzy neural networks
Fuzzy control
18. Chaos, Ecology and Economy and Society (60 pages)
Bifurcations and chaos in ecology / Ihor Lubashevsky
The University of Aizu,, Fukushima, Japan
Marisa Faggini, Dipart di Scienze Economiche e Statistiche, University of Salerno – Fisciano, Italy
Dynamical Traps Caused by Human Fuzzy Rationality
Nonlinear dynamics in spatial systems
Evolution on eco-epidemiological systems
Surviving chaos and change
Why Economics Hasn’t Accomplished What Physics Has?
Oscillations and chaos in dynamic economic models
Control of chaotic population dynamics
Sustainable development
19. Algorithmic Music Composition (20-30 pages)
Chaotic compositions / Scott McLaughlin
University of Leeds (UK)
Dimitrios Sotiropoulos, Technical University of Crete, Chania, Crete, Greece
Nonlinear models and compositions
Deterministic or stochastic models of algorithmic compositions
Mathematical analysis of compositions and applications
Compositions with geometric forms
20. Population Growth: Equilibrium and Chaos in New Extensions of the Verhulst Model (30-50 pages)
The Verhulst Model
The Logistic Parabola, Period Doubling and Self-Similar Symbolic Dy- namics
Periodic Windows Enbedded in Chaos
Differential Models Tied to the Beta Function
Cummulants and Population Dynamics
BetaBoop Functions and Extreme Value Growing Laws
Stability and Population Equilibrium / Dinis Pestana
Department of Statistics and. Operational Research,
University of Lisbon
Lisbon, Portugal
21. Chaos in Language (20 pages)
Language development / Dimitrios Sotiropoulos,
Technical University of Crete, Chania, Crete, Greece
Phonological development
Language learning
Second language acquisition
Language structure
List of Contributors (so far)
Diego Angeli
DIEF - Dipartimento di Ingegneria "Enzo Ferrari", Università degli Studi di Modena e Reggio Emilia, Modena, Italy
Dan-Gheorghe Dimitriu
Faculty of Physics
“Alexandru Ioan Cuza” University of Iasi, Romania
V. P. Drakopoulos
Department of Informatics & Telecommunications
University of Athens
Athens, Greece
Bogdan Epureanu
Department of Mechanical Engineering
University of Michigan
Ann Arbor, MI, USA
Marisa Faggini
Dipartimento di Scienze Economiche e Statistiche
University of Salerno – Fisciano, Italy
Alexander V. Glushkov
Odessa State University-OSENU, Odessa, Ukraine
Avadis Hacinliyan
Department of Physics, Yeditepe University, Kayisdagi, Istanbul, Turkey
N. Jevtic
Bloomsburg University, Bloomsburg, PA, USA
Vladimir L. Kalashnikov,
Institut für Photonik, TU Wien,
Wien Austria
Alexander Kholtygin
Astronomical Institute, Saint-Petersburg University,
Saint-Petersburg, Russia
D. Laroze
Max Planck Institute for Polymer Research, Mainz, Germany
Gennady A. Leonov
Saint-Petersburg State University, Russia
Shijun Liao
State Key Lab of Ocean Engineering
Dept. of Mathematics
School of Naval Architecture, Ocean and Civil Engineering Shanghai Jiao Tong University, Shanghai, China
Ihor Lubashevsky
The University of Aizu,
Fukushima, Japan
Valerio Lucarini
Meteorological Institute
University of Hamburg
Hamburg Germany
Paul Manneville
LadHyX, Hydrodynamics Laboratory, CNRS UMR7646, École Polytechnique - Palaiseau, France
Scott McLaughlin
University of Leeds (UK)
Paul Meehan
Mechanical and Mining Engineering
The University of Queensland, Australia
John Oommen
School of Computer Science, Carleton University
Ottawa, ON, Canada
Dinis Pestana
Department of Statistics and. Operational Research,
University of Lisbon
Lisbon Portugal
S.V. Prants
Pacific Oceanological Institute of the Russian Academy of Sciences,
Vladivostok, Russia
A.G. Ramm
Kansas State University
Kansas, USA
Aleksandr Yu. Shvets
National Technical University of Ukraine "Kyiv Polytechnic Institute
Kyiv, Ukraine
Leszek Sirko
Institute of Physics, Polish Academy of Sciences, Warszawa, Poland
Valentin V. Sokolov
Budker Institute of Nuclear Physics
Theory Department
Novosibirsk, Russia
Charilaos Skiadas
Hanover College,
Hanover, IN, USA
Christos H Skiadas
Technical University of Crete, Chania, Crete, Greece
Dimitrios Sotiropoulos,
Technical University of Crete, Chania, Crete, Greece
Banlue Srisuchinwong
Sirindhorn International Institute of Technology (SIIT)
Bangkadi Thammasat University
Bangkadi Muang, Pathum-Thani Thailand
Mikhail V. Zakrzhevsky
Institute of Mechanics,
Riga Technical University
Riga, Latvia