Regularity and Stochasticity of Nonlinear Dynamical Systems

Description

This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty. Front Matter....Pages i-x Solvability of Some Integro-Differential Equations with Anomalous Diffusion....Pages 1-17 Poincaré Recurrences in Ergodic Systems Without Mixing....Pages 19-49 Success, Hierarchy, and Inequality Under Uncertainty....Pages 51-78 Functional Differential Equations with Piecewise Constant Argument....Pages 79-109 Grazing in Impulsive Differential Equations....Pages 111-159 On Local Topological Classification of Two-Dimensional Orientable, Non-Orientable, and Half-Orientable Horseshoes....Pages 161-180 From Chaos to Order in a Ring of Coupled Oscillators with Frequency Mismatch....Pages 181-198 Dynamics of Some Nonlinear Meromorphic Functions....Pages 199-218 Dynamics of Oscillatory Networks with Pulse Delayed Coupling....Pages 219-246 Bifurcation Trees of Period-3 Motions to Chaos in a Time-Delayed Duffing Oscillator ....Pages 247-262 Travelable Period-1 Motions to Chaos in a Periodically Excited Pendulum....Pages 263-282 Automorphic Systems and Differential-Invariant Solutions....Pages 283-308 Back Matter....Pages 309-311