Symbolic software development for computing the normal form of double Hopf bifurcation.

DOI10.1016/S0895-7177(99)00081-3zbMath1036.34043MaRDI QIDQ1596940

Pei Yu, Qinsheng Bi

Publication date: 5 May 2002

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

zbMATH Keywords

normal formdouble Hopf bifurcation1:1 resonanceexplicit recursive formulas

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Theoretical approximation of solutions to ordinary differential equations (34A45) Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items (8)

Bifurcation analysis for energy transport system and its optimal control using parameter self-tuning law ⋮ Computation of the normal form as well as the unfolding of the vector field with zero-zero-Hopf bifurcation at the origin ⋮ Normal forms of double Hopf oscillators with radial nonlinearities ⋮ Normal form theory and spectral sequences. ⋮ The infinite level normal forms for non-resonant double Hopf singularities ⋮ Bursting behaviors as well as the mechanism of controlled coupled oscillators in a system with double Hopf bifurcations ⋮ Normal forms and nonlocal chaotic behavior in sprott systems ⋮ Leaf-normal form classification for \(n\)-Tuple Hopf singularities

Uses Software

• Maple

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A simple global characterization for normal forms of singular vector fields
• On bifurcation into nonresonant quasi-periodic motions
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Singularities of vector fields
• Unfoldings of certain singularities of vectorfields: Generalized Hopf bifurcations
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• On phase-locked motions associated with strong resonance
• Dynamic behaviour of an autonomous system with three pairs of pure imaginary eigenvalues
• Static and dynamic bifurcations associated with a double-zero eigenvalue
• Free vibration and buckling of shear-deformable cross-ply laminated plates using the state-space concept
• Computation of Normal Forms of Differential Equations Associated with Non-Semisimple Zero Eigenvalues
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