Bifurcation and chaos in escape equation model by incremental harmonic balancing
Periodic motions of the nonlinear system representing the escape equation with cosine and sine parametric excitations and external harmonic excitations are obtained by the incremental harmonic balance (IHB) method. The system contains quadratic stiffness terms. The authors derive explicitly the Jacobian matrix and residue vector for the nonlinearity due to parametric excitation. An arc length path following procedure is used in combination with Floquet theory to trace the response diagram and to investigate the stability of periodic solutions. The system undergoes chaotic motions for increase in the amplitude of harmonic excitation, which is investigated by numerical integration and represented in terms of phase plane, Poincaré sections and Lyapunov exponents. The authors use interpolated cell mapping method to obtain the initial condition map corresponding to two coexisting period 1 motions. The periodic motions and bifurcation points obtained by the IHB method compare very well with results of numerical integration.
scientific article; zbMATH DE number 1486572
scientific article