Dynamical Systems and Methods

Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems presents topics observed at the 3^rd Conference on Nonlinear Science and Complexity(NSC), focusing on energy transfer and synchronization in hybrid nonlinear systems. The studies focus on fundamental theories and principles,analytical and symbolic approaches, computational techniques in nonlinear physical science and mathematics. Broken into three parts, the text covers: Parametrical excited pendulum, nonlinear dynamics in hybrid systems, dynamical system synchronization and (N+1) body dynamics as well as new views different from the existing results in nonlinear dynamics, mathematical methods for dynamical systems including conservation laws, dynamical symmetry in nonlinear differential equations and invex energies and nonlinear phenomena in physical problems such as solutions, complex flows, chemical kinetics, Toda lattices and parallel manipulator.

This book is useful to scholars, researchers and advanced technical members of industrial laboratory facilities developing new tools and products.

Part I: Nonlinear Dynamical Systems.- 1. Mathematical analysis on chaos of a parametrically excited pendulum with damping force.- 2. Energy in hybrid system nonlinear dynamics.- 3.Nonlinear characteristics diagnosis of dynamical systems in engineering.- 4. Synchronization analysis for two coupled populations of phase oscillators.- 5. A Pendulum Synchronizing with a Duffing Oscillator under a Feedback Control.- 6. The Ring Problem of (N+1) Bodies: An Overview.- Part II: Mathematical Methods.- 7. Symbolic computation of conservation laws, generalized symmetries,and recursion operators for nonlinear differential-difference equations.- 8.Approximate polynomial solution of a nonlinear differential equation with Applications in Engineering Problems.- 9. Dynamical Symmetries of Second Order ODE.- 10. Invex Energies on Riemannian Manifolds.- 11. Weyl's Limit Point and Limit Circle Cases for a Dynamic Equation on Time Scales.- 12 Remarks on Suzuki(C)-Condition.- 13.  On the Eigen values of a Non-Hermitian Hamiltonian.- Part III: Nonlinear Physics.- 14 Perturbation methods for solitons and their behavior as particles.- 15. Complex analytic flows.- 16. Unsteady MHD flow past a stretching sheet due to a heat source/sink.- 17.  Effect of chemical kinetics on permeability of a porous rock scaling by concentration of active fluid.- 18. Exciton-phonon dynamics with long range interaction.- 19. Integration of the Finite Toda Lattice with Complex-Valued Initial Data.- 20 Efficient Dynamic Modeling of a Hexa-Type Parallel Manipulator.