Bifurcation and Chaos in Coupled Oscillators
This book develops a general methodological approach to investigate complex physical systems presented by the author in a previous book. The nonlinear dynamics of coupled oscillators is investigated numerically and analytically. Three different mechanical, and one biomechanical, examples are used to demonstrate a general systematical approach to the study of dissipative dynamical systems. Many original examples of special chaotic behavior are discussed and illustrated.
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air stream amplitude analyzed appear Awrejcewicz bifurcation points branch chaotic dynamics chaotic motion chaotic orbits chapter CM CM CM considered constant solutions Cont'd control parameter corresponding coupled oscillators curves degrees of freedom denotes differential equations eigenvalues eigenvectors elastic equations governing equations of motion equilibria example fixed points friction further decrease glottis Hopf bifurcation Hopf bifurcation points human vocal cords increase influence initial value problem investigated Jacobi matrix linear Lyapunov exponent matrix method multipliers Newton's method nonlinear dynamics numerical calculations observed obtain oscilla parametric excitation period doubling periodic solution phase flow phase portrait phase space plane possible power spectra presented qualitatively quasiperiodic attractor rate Q rotor self-excited shown sinusoidally-driven solving stable and unstable stable periodic orbit stick stick-slip Strange Attractors strange chaotic attractor strange non-chaotic attractors subglottis subharmonic subharmonic solution tion traced trajectory trivial solution unit circle values of Q zero