Discontinuity and Complexity in Nonlinear Physical Systems

ISBN-13: 9783319375342 / Angielski / Miękka / 2016 / 433 str.

J. A. Tenreiro Machado; Dumitru Baleanu; Albert C. J. Luo

Opis

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.

Spis treści

In-plane free vibration and stability analysis of high speed rotating disks and rings.- Patent licensing: Stackelberg versus Cournot models.- Privatization and government preferences in a mixed duopoly: Stackelberg versus Cournot.- Nonlinear self-adjointness for some generalized KdV equations.- Conservation Laws for a Family of Benjamin-Bona-Mahony-Burgers equations.- Energy dissipation through viscoelastic chain-based devices.- Simulation of Costas loop in phase-frequency space for general case of signals waveforms.- Simulation of drilling systems models and hidden oscillations.- Dynamical response of a Van der Pol system with an external harmonic excitation and fractional derivative.- Basins of attraction in a simple harvesting system with a stopper.- Milling of composites by recurrence plots and Hilbert-Huang transform.- Formations of Transitional Zones in Shock Wave with Saddle-Node Bifurcations.- Approaches for defining and measuring assembly supply chains complexity.- Tuning of Fractional order PI^lamda D^mu controller with Responce surface methodology.- Chaos in a piecewise linear system with periodic excitation.- 1D Cahn-Hilliard dynamics: coarsening and interrupted coarsening.- Tomographic analysis: a tool for detection and characterization of Lévy flights in chaotic trajectories.- Analytical dynamics of nonlinear rotating blades under parametric excitation.- Dynamical synchronization of two gyroscope systems.- Analytical dynamics of a mass-damper-spring constrained system.- Fractional Maps as Maps with Memory.- New Trends in the Computational Methods in the Fractional Calculus.- Application of the local fractional Fourier series to fractal signals.- Analysis of the DNA Information.

O autorze

José António Tenreiro Machado is Professor, Institute of Engineering, Polytechnic of Porto, Portugal; Dumitru Baleanu is Professor, Department of Mathematics and Computer SciencesCankaya University, Turkey;  Albert Luo is Professor of Mechanical ngineering, Southern Illinois University/Edwardsville, USA

Blurb

This unique book 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.

This book also:

·         Provides Lie group analysis with nonlinear self-adjointness and conservation laws

·         Presents computational methods and control in fractional calculus

·         Discusses discontinuous dynamics and chaos in drilling systems and vibro-impact systems

·         Illustrates the mechanism and dynamics of shock waves and dynamical stability

Discontinuity and Complexity in Nonlinear Physical Systems is an ideal book for scientific researchers, academics, and graduate students in the field of nonlinear dynamics.