Simultaneous equilibrium and heteroclinic bifurcation of planar vector fields via the Melnikov integral
- 1 February 1990
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 3 (1) , 79-99
- https://doi.org/10.1088/0951-7715/3/1/006
Abstract
The author studies the unfoldings of planar vector fields in which a semihyperbolic equilibrium p0 is connected to a hyperbolic saddle q0 by a heteroclinic orbit that lies in the strong unstable manifold of p0. He shows how to produce normal forms for this situation using singularity theory and a version of the Melnikov integral. The normal forms consist of two polynomials, one to describe bifurcation of the semihyperbolic equilibrium and one to describe bifurcation of the heteroclinic orbit.Keywords
This publication has 5 references indexed in Scilit:
- The Riemann problem for 2 × 2 systems of hyperbolic conservation laws with case I quadratic nonlinearitiesJournal of Differential Equations, 1989
- The Saddle-Node Separatrix-Loop BifurcationSIAM Journal on Mathematical Analysis, 1987
- Bifurcation analysis near a double eigenvalue of a model chemical reactionArchive for Rational Mechanics and Analysis, 1981
- Quadratic gradients on the plane are generically Morse-SmaleJournal of Differential Equations, 1979
- Partially hyperbolic fixed pointsTopology, 1971