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Discontinuity and Complexity in Nonlinear Physical Systems

Part of the Nonlinear Systems and Complexity Book Series (volume 6)

Editors: Machado, J. A. Tenreiro; Baleanu, Dumitru; Luo, Albert C J

DOI: 10.1007/978-3-319-01411-1

ISBN: 978-3-319-01410-4

Publisher: Springer International Publishing - Springer Journals

Oct 11, 2013

1 - 10 of 24 Chapters

LitStream

Nonlinear Self-Adjointness for some Generalized KdV Equations

Gandarias, M. L.; Rosa, M.

Pages: 3 –21

[The new concepts of self-adjoint equations formulated in Gandarias (J Phys A: Math Theor 44:262001, 2011) and Ibragimov (J Phys A: Math Theor 44:432002, 2011) are applied to some classes of third order equations. Then, from Ibragimov’s theorem on conservation laws, conservation laws for two...
LitStream

Weak Self-Adjointness and Conservation Laws for a Family of Benjamin-Bona-Mahony-Burgers Equations

Bruzón, M. S.

Pages: 23 –34

[Ibragimov introduced the concepts of self-adjoint and quasi-self-adjoint equations. Gandarias generalized these concepts and defined the concept of weak self-adjoint equations. In this paper we consider a family of Benjamin-Bona-Mahony-Burgers equations and we determine the subclass of equations...
LitStream

Some Analytical Techniques in Fractional Calculus: Realities and Challenges

Baleanu, Dumitru; Wu, Guo-Cheng; Duan, Jun-Sheng

Pages: 35 –62

[In the last decades, much effort has been dedicated to analytical aspects of the fractional differential equations. The Adomian decomposition method and the variational iteration method have been developed from ordinary calculus and become two frequently used analytical methods. In this article,...
LitStream

Application of the Local Fractional Fourier Series to Fractal Signals

Yang, Xiao-Jun; Baleanu, Dumitru; Machado, J. A. Tenreiro

Pages: 63 –89

[Local fractional Fourier series is a generalized Fourier series in fractal space. The local fractional calculus is one of useful tools to process the local fractional continuously non-differentiable functions (fractal functions). Based on the local fractional derivative and integration, the...
LitStream

Parameter Optimization of Fractional Order PIλDμ Controller Using Response Surface Methodology

İskender, Beyza Billur; Özdemir, Necati; Karaoglan, Aslan Deniz

Pages: 91 –105

[This chapter presents optimization of fractional order PIλDμ control parameters by using response surface methodology. The optimization process is observed on a fractional order diffusion system subject to input hysteresis which is defined with Riemann–Liouville fractional derivative. The system...
LitStream

Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative

Syta, Arkadiusz; Litak, Grzegorz

Pages: 107 –112

[We examined the Van der Pol system with external forcing and a memory possessing fractional damping term. Calculating the basins of attraction we showed broad spectrum of nonlinear behaviour connected with sensitivity to the initial conditions. To quantify dynamical response of the system we...
LitStream

Fractional Calculus: From Simple Control Solutions to Complex Implementation Issues

Muresan, Cristina I.

Pages: 113 –134

[Fractional calculus is currently gaining more and more popularity in the control engineering world. Several tuning algorithms for fractional order controllers have been proposed so far. This chapter describes a simple tuning rule for fractional order PI controllers for single-input–single-output...
LitStream

Emerging Tools for Quantifying Unconscious Analgesia: Fractional-Order Impedance Models

Chevalier, Amélie; Copot, Dana; Ionescu, Clara M.; Machado, J. A. Tenreiro; De Keyser, Robin

Pages: 135 –149

[This paper presents the application of model-based predictive control (MPC) in combination with a sensor for the measurement of analgesia (pain relief) in an unconscious patient in order to control the level of anesthesia. The MPC strategy uses fractional-order impedance models (FOIMs) to model...
LitStream

1D Cahn–Hilliard Dynamics: Coarsening and Interrupted Coarsening

Villain-Guillot, Simon

Pages: 153 –168

[Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects.In all models with local interactions, these ordered phases disappear in the strong...
LitStream

Nonlinear Analysis of Phase-locked Loop-Based Circuits

Best, R. E.; Kuznetsov, N. V.; Leonov, G. A.; Yuldashev, M. V.; Yuldashev, R. V.

Pages: 169 –192

[Main problems of simulation and mathematical modeling of high-frequency signals for analog Costas loop and for analog phase-locked loop (PLL) are considered. Two approachers which allow to solve these problems are considered. In the first approach, nonlinear models of classical PLL and classical...

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