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 Introduction 1.A Chaos and Nonlinear Dynamics (60 pages) Nonlinear dynamics of continuous, discontinuous and hybrid systems 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 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 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 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 E Fractals (50 pages) Fractals and self-similarity (The Cantor set, the Sierpinski carpet,…) 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 Bogdan Epureanu, Dept of Mech Engineering University of Michigan, Ann Arbor, MI, USA A.G Ramm, Kansas State University Kansas, USA Valerio Lucarini, Meteorological Institute University of Hamburg, Germany 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 Avadis Hacinliyan Department of Physics, Yeditepe University, Kayisdagi, Istanbul, Turkey Gennady A Leonov-Nikolay Kuznetsov Saint-Petersburg State University, Russia V P Drakopoulos Department of Informatics & Telecommunications University of Athens Athens, Greece 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 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 nonideal 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) Stochastic Chaos (40 pages) Stochastic Chaos versus Deterministic 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 Spatiotemporal Chaos (60-80 pages) Reaction diffusion patterns 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 Data Analysis and Chaos (50 pages) Analysis of chaotic data 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 Hydrodynamics and Turbulence (50 pages) Turbulence Turbulent Transport and Simulation Reliable numerical modelling of complex dynamics in confined Mikhail V Zakrzhevsky Institute of Mechanics, Riga Technical University, Riga, Latvia Aleksandr Yu Shvets National Technical University of Ukraine "Kyiv Polytechnic Institute Kyiv, Ukraine Christos H Skiadas, Technical University of Crete, Chania, Crete, Greece Paul Manneville LadHyX, Hydrodynamics Laboratory, CNRS UMR7646, École Polytechnique - Palaiseau, France Avadis Hacinliyan Department of Physics, Yeditepe University, Kayisdagi, Istanbul, Turkey Alexander V Glushkov Odessa State University-OSENU, Odessa, Ukraine Diego Angeli DIEF - Dipartimento di Ingegneria "Enzo Ferrari", thermal flows Entropy of particles on a turbulent sea Fluid Mechanics and Turbulence Chaotic advection Chaotic advection in oscillatory flows Optics and Chaos (30 pages) Nonlinear optics The optical rogue waves Laser optics and chaos The Ikeda attractor Quantum chaos Chaotic Oscillations and Circuits (60-80 pages) Chaotic delay equations 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 Università degli Studi di Modena e Reggio Emilia, Modena, Italy Vladimir L Kalashnikov, Institut für Photonik, TU Wien, Wien Austria 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 Chaos in Climate Dynamics (30 pages) Chaos in simplified Climate Models (The Lorenz model) Weather forecasts Earth's climate Geophysical Flows (40 pages) Geodesic flows 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 S.V Prants Pacific Oceanological Institute of the Russian Academy of Sciences, Vladivostok, Russia 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 Flow equations for Hamiltonians Hamiltonian and Quantum Chaos Valentin V Sokolov Budker Institute of Nuclear Physics Theory Department Novosibirsk, Russia 13 Chaos in Astronomy and Astrophysics (50-70 pages) Chaos in the Solar system 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 Complex space charge structures in plasma Oscillations and instabilities in plasma Laser ablation plasma Alexander Kholtygin Astronomical Institute, Saint-Petersburg University, Saint-Petersburg, Russia N Jevtic Bloomsburg University, Bloomsburg, PA, USA Dan-Gheorghe Dimitriu Faculty of Physics “Alexandru Ioan Cuza” University of Iasi, Romania 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 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 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 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 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 D Laroze Max Planck Institute for Polymer Research, Mainz, Germany John Oommen School of Computer Science, Carleton University Ottawa, ON, Canada Ihor Lubashevsky The University of Aizu,, Fukushima, Japan Marisa Faggini, Dipart di Scienze Economiche e Statistiche, University of Salerno – Fisciano, Italy Scott McLaughlin University of Leeds (UK) Dimitrios Sotiropoulos, Technical University of Crete, Chania, Crete, Greece Dinis Pestana Department of Statistics and Operational Research, University of Lisbon Lisbon, Portugal BetaBoop Functions and Extreme Value Growing Laws Stability and Population Equilibrium 21 Chaos in Language (20 pages) Language development Phonological development Language learning Second language acquisition Language structure Dimitrios Sotiropoulos, Technical University of Crete, Chania, Crete, Greece 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, SaintPetersburg 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