Analytical routes to chaos in nonlinear engineering discusses analytical solutions of periodic motions to chaos or quasi periodic motions in nonlinear dynamical systems in engineering and considers engineering applications design and control it systematically discusses complex nonlinear phenomena in engineering nonlinear systems including the periodically forced duffing oscillator . Analytical routes to chaos in nonlinear engineering discusses analytical solutions of periodic motions to chaos or quasi periodic motions in nonlinear dynamical systems in engineering and considers engineering applications design and control it systematically discusses complex nonlinear phenomena in engineering nonlinear systems including the periodically forced duffing oscillator . Analytical routes to chaos in nonlinear engineering may 2014 doi 101002 9781118883938 authors albert cj luo 43 southern illinois university edwardsville download full text pdf read full . Analytical bifurcation trees of period 1 motions to chaos will be presented the hopf bifurcation of periodic motion can cause not only the bifurcation tree but quasi periodic motions displacement orbits of periodic motions in nonlinear rotor systems show motion complexity and harmonic amplitude spectrums gives harmonic effects on periodic motions analytical routes to chaos in nonlinear