Discontinuity and Complexity in Nonlinear Physical Systems

✍ Scribed by M. L. Gandarias, M. Rosa (auth.), J. A. Tenreiro Machado, Dumitru Baleanu, Albert C J Luo (eds.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 433
• Series: Nonlinear Systems and Complexity 6
• Edition: 1
• Category: Library

✦ Synopsis

Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.

✦ Table of Contents

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Nonlinear Self-Adjointness for some Generalized KdV Equations....Pages 3-21
Weak Self-Adjointness and Conservation Laws for a Family of Benjamin-Bona-Mahony-Burgers Equations....Pages 23-34
Some Analytical Techniques in Fractional Calculus: Realities and Challenges....Pages 35-62
Application of the Local Fractional Fourier Series to Fractal Signals....Pages 63-89
Parameter Optimization of Fractional Order PI λ D μ Controller Using Response Surface Methodology....Pages 91-105
Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative....Pages 107-112
Fractional Calculus: From Simple Control Solutions to Complex Implementation Issues....Pages 113-134
Emerging Tools for Quantifying Unconscious Analgesia: Fractional-Order Impedance Models....Pages 135-149
Front Matter....Pages 151-151
1D Cahn–Hilliard Dynamics: Coarsening and Interrupted Coarsening....Pages 153-168
Nonlinear Analysis of Phase-locked Loop-Based Circuits....Pages 169-192
Approaches to Defining and Measuring Assembly Supply Chain Complexity....Pages 193-213
Non-commutative Tomography: Applications to Data Analysis....Pages 215-254
Projective Synchronization of Two Gyroscope Systems with Different Motions....Pages 255-272
Measuring and Analysing Nonlinearities in the Lung Tissue....Pages 273-283
Front Matter....Pages 285-285
Drilling Systems: Stability and Hidden Oscillations....Pages 287-304
Chaos in a Piecewise Linear System with Periodic Oscillations....Pages 305-313
Basins of Attraction in a Simple Harvesting System with a Stopper....Pages 315-321
Analytical Dynamics of a Mass–Damper–Spring Constrained System....Pages 323-343
Front Matter....Pages 345-345
Formations of Transitional Zones in Shock Wave with Saddle-Node Bifurcations....Pages 347-358
Dynamics of Composite Milling: Application of Recurrence Plots to Huang Experimental Modes....Pages 359-367
Front Matter....Pages 345-345
The Dynamics of Shear-Type Frames Equipped with Chain-Based Nonlinear Braces....Pages 369-388
In-Plane Free Vibration and Stability of High Speed Rotating Annular Disks and Rings....Pages 389-408
Patent Licensing: Stackelberg Versus Cournot Models....Pages 409-420
Privatization and Government Preferences in a Mixed Duopoly: Stackelberg Versus Cournot....Pages 421-430
Back Matter....Pages 431-433

✦ Subjects

Complexity; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics