Last updated: 14 March 2013 Handbook of Applications of Chaos Theory (~1100 pages) Table of Contents



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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. Introduction










1.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





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