Discontinuity and Complexity in Nonlinear Physical Systems [Hardcover]

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.This book provides Lie group analysis with nonlinear self-adjointess and conservation laws. It presents computational methods and control in fractional calculus as well as discusses discontinuous dynamics and chaos in drilling systems and vibro-impact systems.?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 derivl£P