Bifurcations of the phase pattern of an equation system arising in the problem of stability loss of selfoscillations close to 1:4 resonance

DOI10.1016/0021-8928(78)90036-9zbMath0419.58013OpenAlexW1542299046MaRDI QIDQ1132440

Anatoly I. Neishtadt

Publication date: 1979

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8928(78)90036-9

zbMATH Keywords

loss of stability of a periodic solution close to 1:4 resonance

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Perturbations of ordinary differential equations (34D10) Stability theory for smooth dynamical systems (37C75) Local and nonlocal bifurcation theory for dynamical systems (37G99) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (5)

New criteria for the monotonicity of the ratio of two abelian integrals ⋮ Bifurcations of certain family of planar vector fields tangent to axes ⋮ On the bifurcation of separatrices in the problem of stability loss of auto-oscillations near 1:4 resonance ⋮ Limit cycles for 3-monomial differential equations ⋮ Microbial predation in a periodically operated chemostat: A global study of the interaction between natural and externally imposed frequencies

Cites Work

• Versal deformation of a singular point of a vector field on the plane in the case of zero eigenvalues
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
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