Discontinuity and Complexity in Nonlinear Physical Systems - Machado, J. A. Tenreiro; Baleanu, Dumitru; Luo, Albert C J. (Nonlinear Systems and Complexity, 2014)
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.