The cusp of order n

DOI10.1016/0022-0396(90)90105-XzbMath0721.34020MaRDI QIDQ2640749

Pierre Joyal

Publication date: 1990

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

cuspsingular pointslimit cyclesdynamical systemsChebyshev systemsbifurcation diagramMelnikov method

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Dynamical systems and ergodic theory (37-XX)

Related Items

Limit cycle bifurcations in a class of piecewise smooth systems with a double homoclinic loop, Versal unfolding of a nilpotent Liénard equilibrium within the odd Liénard family, Bogdanov-Takens bifurcation of codimensions 3 and 4 in a Holling and Leslie type predator-prey system with strong Allee effect, Abelian Integrals from an Unfolding of Codimension-3 Singularities with Nilpotent Linear Part, Bifurcation of limit cycles and the cusp of ordern, Abelian integrals in unfoldings of codimension 3 singularities with nilpotent linear parts, HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS, Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles, Local bifurcations and codimension-3 degenerate bifurcations of a quintic nonlinear beam under parametric excitation, Some Bifurcation Analysis in a Family of Nonsmooth Liénard Systems, MULTIPLE BIFURCATIONS IN A PREDATOR–PREY SYSTEM OF HOLLING AND LESLIE TYPE WITH CONSTANT-YIELD PREY HARVESTING, Multiple bifurcations in a predator-prey system of modified Holling and Leslie type with double Allee effect and nonlinear harvesting

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Elliptic integrals and their nonoscillation
• A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4
• Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
• Generalized Hopf Bifurcation and Its Dual Generalized Homoclinic Bifurcation