FDA Express (Vol.2, No.6, Mar.30, 2012)

FDA Express    Vol. 2, No. 6, Mar. 30, 2012

Editors: W. Chen    H.G. Sun    X.D. Zhang    S. Hu
Institute of Soft Matter Mechanics, Hohai University
For contribution:
fdaexpress@hhu.edu.cn
For subscription: http://em.hhu.edu.cn/fda/subscription.htm

↑  Conferences

       Notice for FDA2012 Awards

  Books

       Distributed-Order Dynamic Systems
       SCALE RELATIVITY AND FRACTAL SPACE-TIME - A New Approach to Unifying Relativity and Quantum Mechanics

↑  Journals

       Chaos, Solitons & Fractals

       International Journal of Bifurcation and Chaos
  Classical Papers
       A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity

 Researchers & Groups

       Prof. Fawang Liu
 

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 Conferences
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Notice for FDA2012 Awards

By now, the Fifth IFAC symposium on Fractional Differentiation and its Application (FDA12) has received 321 abstracts and 235 full papers covering most research fields of fractional calculus. We expect a successful FDA12 ahead.

The award committee of the FDA12 is still soliciting the nomination and application of the awards, which recognize and reward excellence in the following four categories:

1.       Mittag-Leffler Award: FDA Achievement Award

2.       Riemann-Liouville Awards: Best FDA Papers (theory, application)

3.       Gr邦nwald-Letnikov Awards: Best Student Papers (theory, application)

4.       FDA Dissemination Award

All participants are welcome to nominate or apply these Awards, especially for the Best Student Papers Awards and Best FDA Papers Awards. We strongly encourage young and junior researchers to join the competition for the best student paper awards under the condition that the student has to be the major contributor and will participate in the FDA12 to present the paper. If you intend to nominate or apply an award, please email the name, paper number and paper title to us as soon as possible to fda12@hhu.edu.cn and sun.fda2012@gmail.com. More information about these Awards can refer to http://em.hhu.edu.cn/fda12/Awards.html.

The deadline for Award application is April 7, 2012.

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Books

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Distributed-Order Dynamic Systems

Zhuang Jiao, YangQuan Chen, Igor Podlubny 

http://www.springer.com/engineering/control/book/978-1-4471-2851-9

Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems. This Brief will broaden the toolbox available to researchers interested in modeling, analysis, control and filtering. It contains contextual material outlining the progression from integer-order, through fractional-order to distributed-order systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant-, integer-, and distributed-order treatments. The power of the distributed-order model is demonstrated with work on the stability of noncommensurate-order linear time-invariant systems. Generic applications of the distributed-order operator follow: signal processing and viscoelastic damping of a mass每spring set up. A new general approach to discretization of distributed-order derivatives and integrals is described. The Brief is rounded out with a consideration of likely future research and applications and with a number of MATLAB® codes to reduce repetitive coding tasks and encourage new workers in distributed-order systems.

Keywords: Distributed-order Control - Distributed-order Linear Time-invariant Systems - Distributed-order Modelling - Distributed-order Signal Processing - Fractional-order systems - Numerical Solution of Distributed-order Equations

Related subjects: Applications - Control Engineering - Energy - Signals & Communication

Table of contents

l        Introduction

l        Distributed-Order Linear Time-Invariant System (DOLTIS) and Its Stability Analysis

l        Noncommensurate Constant Orders as Special Cases of DOLTIS.

l        Distributed-Order Filtering and Distributed-Order Optimal Damping

l        Numerical Solution of Differential Equations of Distributed Order

l        Future Topics  

l        Appendix: MATLAB Codes

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SCALE RELATIVITY AND FRACTAL SPACE-TIME
- A New Approach to Unifying Relativity and Quantum Mechanics

http://www.worldscibooks.com/physics/p752.html

Laurent Nottale

This book provides a comprehensive survey of the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling the basis of quantum mechanics on the principle of relativity, provided this principle is extended to scale transformations of the reference system. In the framework of such a newly generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that unifies and thus goes beyond the classical and quantum regimes taken separately. A related concern of this book is the geometry of space-time, which is described as being fractal and non differentiable. It collects and organizes theoretical developments and applications in many fields, including physics, mathematics, astrophysics, cosmology and life sciences.

Contents:

 Readership: Academics, post-graduates and professionals interested in astrophysics and cosmology.

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Journals

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Chaos, Solitons & Fractals

Volume 45, Issue 4 (2012)

Coupled polariton solitons in semiconductor microcavities with a double-well potential

W.L. Zhang, Y.J. Rao

 

M-ary signal detection via a bistable system in the presence of L谷vy noise

Lingzao Zeng, Jianlong Li, Jiachun Shi

 

Effect of asynchronous updating on the stability of cellular automata

J.M. Baetens, P. Van der Weeën, B. De Baets

 

Strategy changing penalty promotes cooperation in spatial prisoner*s dilemma game

Qing Jin, Zhen Wang, Zhen Wang, Yi-Ling Wang

 

Nonlinear quantum dynamics in diatomic molecules: Vibration, rotation and spin

Ciann-Dong Yang, Hung-Jen Weng

 

The stability of distributed neutral delay differential systems with Markovian switching

R. Ravi Kumar, Kil To Chong

 

Switching induced complex dynamics in an extended logistic map

Erik A. Levinsohn, Steve A. Mendoza, Enrique Peacock-L車pez

 

Fiscal policy lags and income adjustment processes

Luigi De Cesare, Mario Sportelli

 

Mixing properties of set-valued maps on hyperspaces via Furstenberg families

Heman Fu, Zhitao Xing

 

A family of integrable differential每difference equations, its bi-Hamiltonian structure and binary nonlinearization of the Lax pairs and adjoint Lax pairs

Xi-Xiang Xu

 

Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems

Feng Liang, Maoan Han

 

The discontinuous flat top tent map and the nested period incrementing bifurcation structure

Ben Futter, Viktor Avrutin, Michael Schanz

 

Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays

P. Balasubramaniam, S. Lakshmanan, A. Manivannan

 

Global exponential synchronization criterion for switched linear coupled dynamic networks

Zhi Li

 

Differential form method for finding symmetries of a (2 + 1)-dimensional Camassa每Holm system based on its Lax pair

Na Lv, Jian-Qin Mei, Hong-Qing Zhang

 

Nonlinear delay monopoly with bounded rationality

Akio Matsumoto, Ferenc Szidarovszky

 

Some fixed point results for a generalized 肉-weak contraction mappings in orbitally metric spaces

Wasfi Shatanawi

 

Possibilities of introducing different functional circuits on top of a structural neuron triplet: Where do the gains lie?

Igor Franović, Vladimir Miljković

 

Parameters identification of chaotic system by chaotic gravitational search algorithm

Chaoshun Li, Jianzhong Zhou, Jian Xiao, Han Xiao

 

Delay-induced diversity of firing behavior and ordered chaotic firing in adaptive neuronal networks

Yubing Gong, Li Wang, Bo Xu

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International Journal of Bifurcation and Chaos

Volume 22, Issue 2 (February 2012)

THEME SECTION: Complex Systems and Applications

 

INTRODUCTION

M. A. Aziz-Alaoui, Cyrille Bertelle and Xinzhi Liu

 

THEME SECTION: Complex Systems and Applications 〞 Tutorials and Reviews

 

HUN TUN VERSUS BIG BANG: HOW CLASSICAL CHAOS IMPLIES BOTH "THERMODYNAMICS" AND "CRYODYNAMICS"

Otto E. Rössler

 

ACTIVE NETWORKS THAT MAXIMIZE THE AMOUNT OF INFORMATION TRANSMISSION

M. S. Baptista, J. X. De Carvalho, M. S. Hussein and C. Grebogi

 

THEME SECTION: Complex Systems and Applications 〞 Papers

 

EMERGENCE OF RANDOMNESS FROM CHAOS

R. Lozi

 

CONNECTING PERIOD-DOUBLING CASCADES TO CHAOS

Evelyn Sander and James A. Yorke

 

COMPLEX DYNAMICS OF ELEMENTARY CELLULAR AUTOMATA EMERGING FROM CHAOTIC RULES

Genaro J. Mart赤nez, Andrew Adamatzky and Ramon Alonso-Sanz

 

ON SOME RECENT ADVANCES IN COMPLEX SOFTWARE NETWORKS: MODELING, ANALYSIS, EVOLUTION AND APPLICATIONS

Hongchun Wang, Keqing He, Bing Li and Jinhu L邦

 

MODELING THE DYNAMICS OF COMPLEX INTERACTION SYSTEMS: FROM MORPHOGENESIS TO CONTROL

N. Corson, M. A. Aziz-Alaoui, R. Ghnemat, S. Balev and C. Bertelle

 

CANARD CYCLES IN GLOBAL DYNAMICS

Alexandre Vidal and Jean-Pierre Françoise

 

QUANTIFYING CHANGES IN THE SPATIAL STRUCTURE OF TRABECULAR BONE

Norbert Marwan, Gise Beller, Dieter Felsenberg, Peter Saparin and J邦rgen Kurths

 

ZERO-DIFFUSION DOMAINS IN REACTION每DIFFUSION MORPHOGENETIC AND EPIDEMIOLOGIC PROCESSES

Jacques Demongeot, Jean Gaudart, Athanasios Lontos, Julie Mintsa, Emmanuel Promayon and Mustapha Rachdi

 

EFFECTS OF REFUGES AND DENSITY DEPENDENT DISPERSAL ON INTERSPECIFIC COMPETITION DYNAMICS

Nguyen-Ngoc Doanh, Nguyen-Huu Tri and Auger Pierre

 

DYNAMICS UNDERLYING PATIENT-VENTILATOR INTERACTIONS DURING NOCTURNAL NONINVASIVE VENTILATION

R. Naeck, D. Bounoiare, U. S. Freitas, H. Rabarimanantsoa, A. Portmann, F. Portier, A. Cuvelier, J.-F. Muir and C. Letellier

 

ROBUST SENSOR FAULT RECONSTRUCTION FOR NONLINEAR SYSTEMS USING OBSERVERS

Changfan Zhang, Xinzhi Liu and Jing He

 

PARTIAL CONTROL OF TRANSIENT CHAOS IN ELECTRONIC CIRCUITS

Alexandre Wagemakers, Samuel Zambrano and Miguel A. F. Sanju芍n

 

MULTI-SCROLL CHAOTIC AND HYPERCHAOTIC ATTRACTORS GENERATED FROM CHEN SYSTEM

Xinzhi Liu, Xuemin (Sherman) Shen and Hongtao Zhang

 

Tutorials and Reviews

 

CHARACTERIZING NONLINEAR SPATIO-TEMPORAL SYSTEMS IN THE FREQUENCY DOMAIN

Yuzhu Guo, L. Z. Guo, S. A. Billings, Daniel Coca and Z. Q. Lang

 

Papers

 

BIFURCATION IN A PIECEWISE LINEAR CIRCUIT WITH SWITCHING BOUNDARIES

Zhengdi Zhang and Qinsheng Bi

 

CLASSIFYING WITH A TWO NEURON CNN

Mireia Vinyoles-Serra and Xavier Vilas赤s-Cardona

 

BIFURCATION AND CONTROL IN AN INERTIAL TWO-NEURON SYSTEM WITH TIME DELAYS

Hong Yong Zhao, Xiao Hong Yu and Ling Wang

 

STABILITY AND BIFURCATION ANALYSIS IN A DIFFUSIVE BRUSSELATOR SYSTEM WITH DELAYED FEEDBACK CONTROL

Wenjie Zuo and Junjie Wei

 

RESEARCH ON THE GALLOPING AND ANTI-GALLOPING OF THE TRANSMISSION LINE

Zhaohong Qin, Yushu Chen, Xueping Zhan, Bin Liu And Kuanjun Zhu

 

EXAMPLES OF THE EFFECT OF GROWTH AND STRAIN ON TURING PATTERN FORMATION DYNAMICS

Diego Alexander Garz車n-Alvarado

 

DYNAMICS AND BIFURCATIONS OF A NONHOLONOMIC HEISENBERG SYSTEM

M車nica Molina-Becerra, Jorge Gal芍n-Vioque and Emilio Freire

 

A NOVEL RESULT IN THE FIELD OF NONLINEAR STABILITY ANALYSIS OF BOILING WATER REACTORS

Carsten Lange, Dieter Hennig and Antonio Hurtado

 

ANALYSIS OF NEW FOUR-DIMENSIONAL CHAOTIC CIRCUITS WITH EXPERIMENTAL AND NUMERICAL METHODS

Guo-Qing Huang and Xin Wu

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Classical Papers
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A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity

R. L. Bagley and P. J. Torvik


Publication information: R. L. Bagley and P. J. Torvik: A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity. Journal of Rheology, 27, 201 (1983); http://dx.doi.org/10.1122/1.549724.

This article establishes a link between molecular theories that predict the macroscopic behavior of certain viscoelastic media and an empirically developed fractional calculus approach to viscoelasticity. The molecular theory addresses the viscoelastic properties of polymer solids with no crosslinking. It is shown that the results of these molecular theories are equivalent to constitutive relationships written in terms of the fractional calculus. Such relationships, developed previously from an empirical base, have been shown to be useful tools for engineering analyses. The establishment of a theoretical basis for these new constitutive relationships enhances their value, as they may now be used with increased confidence.

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Researchers & Groups
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Prof. Fawang Liu

Queensland University of Technology, Australia

Professor Fawang Liu received his MSc from Fuzhou University in 1982 and PhD from Trinity College, Dublin, Ireland in 1991, respectively. Since graduation, he has been working in computational and applied mathematics at Fuzhou University, Xiamen University, Trinity College Dublin (Ireland), University College Dublin (Ireland), University of Queensland (Australia) and Queensland University of Technology (Australia ) for over thirty years. Now he is working at Queensland University of Technology, Australia (since 1991). Professor Liu has made important contributions to the field including fractional differential equations, anomalous diffusion, parameter estimation for fractional dynamical models arising from biological systems,  semiconductor device equations, microwave heating problems, gas-solid reactions, singular perturbation problem and saltwater intrusion into aquifer systems, particularly in numerical methods and theoretical analysis. He has supervised over thirteen PhD students and eleven MSc students on these fields.  Professor Liu is a leading researcher in the numerical methods and numerical analysis of fractional differential equations. Professor Liu has received various awards of his contributions in the field of fractional calculus and singular perturbation problem. Professor Liu is a member of the editorial board of some international journals and is a Lead Guest Editor of the special issue on fractional differential equations (I) in 2010 and (II) in 2011 of the International Journal of Differential Equations. He has published over 170 papers in these fields.

Selected Papers

Liu F., Burrage K., Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. COMPUTERS & MATHEMATICS WITH APPLICATIONS, Vol. 62, No. 3, Special issue: SI, pp. 822-833  DOI: 10.1016/j.camwa.2011.03.002, 2011.

Liu Fawang, Yang Qianqian, Turner Ian, Two New Implicit Numerical Methods for the Fractional Cable Equation. JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, Vol. 6, No. 1, DOI: 10.1115/1.4002269,  2011.

Yang Q., Liu F., Turner I., Numerical methods for fractional partial differential equations with Riesz space fractional derivatives. APPLIED MATHEMATICAL MODELLING, Vol. 34, No. 1, pp. 200-218  DOI: 10.1016/j.apm.2009.04.006, 2010.

Chen Chang-Ming, Liu F., Anh V., A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol. 223, No. 2, pp. 777-789  DOI: 10.1016/j.cam.2008.03.001, 2009.

Zhuang P., Liu F., Anh V., et al., NUMERICAL METHODS FOR THE VARIABLE-ORDER FRACTIONAL ADVECTION-DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM. SIAM JOURNAL ON NUMERICAL ANALYSIS, Vol. 47, No. 3, pp. 1760-1781  DOI: 10.1137/080730597, 2009.

Chen S., Liu F., Zhuang P., et al., Finite difference approximations for the fractional Fokker-Planck equation. APPLIED MATHEMATICAL MODELLING, Vol. 33, No. 1, pp. 256-273, DOI: 10.1016/j.apm.2007.11.005, 2009. 

Chen Chang-ming, Liu F., Burrage K., Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation. APPLIED MATHEMATICS AND COMPUTATION, Vol. 198, No. 2, pp. 754-769. DOI: 10.1016/j.amc.2007.09.020, 2008.

Yu Q., Liu F., Anh V., et al., Solving linear and non-linear space-time fractional reaction-diffusion equations by the Adomian decomposition method. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Vol. 74, No. 1, pp. 138-158  DOI: 10.1002/nme.2165, 2008.

Chen J., Liu F., Anh V., Analytical solution for the time-fractional telegraph equation by the method of separating variables. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Vol. 338, No. 2, pp. 1364-1377, DOI: 10.1016/j.jmaa.2007.06.023, 2008.

Chen Chang-Ming, Liu F., Turner I., A Fourier method for the fractional diffusion equation describing sub-diffusion. JOURNAL OF COMPUTATIONAL PHYSICS, Vol. 227, No. 2, pp. 886-897  DOI: 10.1016/j.jcp.2007.05.012, 2007.

Liu F., Zhuang P., Anh V., et al., Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. APPLIED MATHEMATICS AND COMPUTATION, Vol. 191, No. 1, pp. 12-20, DOI: 10.1016/j.amc.2006.08.162, 2007.

Lin R., Liu F. Fractional high order methods for the nonlinear fractional ordinary differential equation. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. Vol. 66, No. 4, pp. 856-869, DOI: 10.1016/j.na.2005.12.027, 2007.

Huang F, Liu F. The time fractional diffusion equation and the advection-dispersion equation. ANZIAM JOURNAL, Vol. 46, Part 3, pp. 317-330, 2005.

Liu F, Anh V, Turner I. Numerical solution of the space fractional Fokker-Planck equation. Conference: International Conference on Boundary and Interior Layers (BAIL 2002), Univ Western Australia, Perth, AUSTRALIA, JUL 08-12, 2002. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol. 166, No. 1, pp. 209-219  DOI: 10.1016/j.cam.2003.09.028, 2004.

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