Bifurcation and chaos in escape equation model by incremental harmonic balancing

DOI10.1016/S0960-0779(99)00044-2zbMath0962.70023MaRDI QIDQ1573965

N. Delaunay

Publication date: 9 August 2000

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

zbMATH Keywords

numerical integrationPoincaré sectionsbifurcationLyapunov exponentsFloquet theoryJacobian matrixphase planechaotic motionsincremental harmonic balance methodstability of periodic solutionsarc length path following procedureescape equationinterpolated cell mapping methodparametric excitationsquadratic stiffness terms

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Bifurcations and instability for nonlinear problems in mechanics (70K50) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55)

Related Items (4)

Bifurcation and route-to-chaos analyses for Mathieu-Duffing oscillator by the incremental harmonic balance method ⋮ A modified incremental harmonic balance method based on the fast Fourier transform and Broyden's method ⋮ Computation of periodic orbits for piecewise linear oscillator by harmonic balance methods ⋮ Nonlinear vibrations of dynamical systems with a general form of piecewise-linear viscous damping by incremental harmonic balance method

Cites Work

• Suppression of steady state bifurcations and premature fractal basin erosion in nonlinear systems subjected to combined external and parametric excitations
• On minimum safe impulsive velocity in the driven escape oscillator
• Non-linear vibration of coupled duffing oscillators by an improved incremental harmonic balance method
• Fractal erosion of basins of attraction in coupled non-linear systems
• Fractal control boundaries of driven oscillators and their relevance to safe engineering design
• Integrity measures quantifying the erosion of smooth and fractal basins of attraction
• Interpolated Cell Mapping of Dynamical Systems
• A Variable Parameter Incrementation Method for Dynamic Instability of Linear and Nonlinear Elastic Systems
• Indeterminate jumps to resonance from a tangled saddle-node bifurcation
• Mechanics of ship capsize under direct and parametric wave excitation
• Indeterminate trans-critical bifurcations in parametrically excited systems
• Indeterminate sub-critical bifurcations in parametric resonance
• Jumps to Resonance: Long Chaotic Transients, Unpredictable Outcome, and the Probability of Restabilization

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