A paradigmatic system to study the transition from zero/Hopf to double-zero/Hopf bifurcation

DOI10.1007/s11071-012-0435-xzbMath1267.34067OpenAlexW2039272167MaRDI QIDQ354045

Daniele Zulli, Angelo Luongo

Publication date: 17 July 2013

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-012-0435-x

zbMATH Keywords

Hopf bifurcationmultiple scale methodcodimension-3 bifurcationdouble-zero bifurcation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Numerical methods for ordinary differential equations (65L99) Multifrequency systems of ordinary differential equations (34C46)

Related Items

Some research perspectives in galloping phenomena: critical conditions and post-critical behavior ⋮ On the contribution of Angelo Luongo to mechanics: in honor of his 60th birthday ⋮ Galloping of internally resonant towers subjected to turbulent wind ⋮ The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence ⋮ Stability and bifurcation for limit cycle oscillations of an airfoil with external store ⋮ Invariant subspace reduction for linear dynamic analysis of finite-dimensional viscoelastic structures ⋮ Aeroelastic instability analysis of NES-controlled systems via a mixed multiple scale/harmonic balance method ⋮ Asymptotic analysis of a noncontact AFM microcantilever sensor with external feedback control ⋮ Zero-Hopf bifurcation in the Van der Pol oscillator with delayed position and velocity feedback ⋮ Stabilization via parametric excitation of multi-dof statically unstable systems ⋮ Limitation on the method of strained coordinates for vibrations with weak grazing unilateral contact ⋮ Modeling the linear dynamics of continuous viscoelastic systems on their infinite-dimensional central subspace

Uses Software

• AUTO
• AUTO-07P

Cites Work

• Unnamed Item
• Unnamed Item
• The regions of flutter and divergence instability of a column subjected to Beck's generalized load, taking into account the torsional flexibility of the loaded end of the column
• Bifurcations and transition phenomena in an impact oscillator.
• Coupled Van der Pol-Duffing oscillators: phase dynamics and structure of synchronization tongues
• Properties of synchronization in the systems of non-identical coupled van der Pol and van der Pol-Duffing oscillators. Broadband synchronization
• Dynamical analysis of two coupled parametrically excited van der Pol oscillators
• Nonlinear targeted energy transfer in mechanical and structural systems. 2 Vols.
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The transition from phase locking to drift in a system of two weakly coupled Van Der Pol oscillators
• Determination of the limit of initiation of self-excited vibration of rotors
• Bifurcation of periodic motions in two weakly coupled van der Pol oscillators
• Dynamics of two strongly coupled van der Pol oscillators
• Resonance behaviour and jump phenomenon in a two coupled Duffing-van der Pol oscillators
• Divergence and flutter of nonconservative systems with intermediate support
• A mathematical framework for critical transitions: bifurcations, fast-slow systems and stochastic dynamics
• Bifurcations to divergence and flutter in flow-induced oscillations: A finite dimensional analysis
• Eigensolutions sensitivity for nonsymmetric matrices with repeated eigenvalues
• MULTIPLE SCALE ANALYSIS FOR DIVERGENCE-HOPF BIFURCATION OF IMPERFECT SYMMETRIC SYSTEMS