The second part of Hilbert's 16th problem deals with polynomial differential equations in the
plane. It remains unsolved even for quadratic polynomials. There were several attempts to …

The total number of such permutations is equal to (n—1)(«—2)/2. Some of them are rotations
(isomorphic to the addition of a constant to the residues modn). But it is not clear what …

Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a
talk" Mathematical problems" at the Second Interna tional Congress of Mathematicians in …

The paper deals with Liénard equations of the form x= y, y= P (x)+ yQ (x) with P and Q
polynomials of degree respectively 3 and 2. Attention goes to perturbations of the …

We derive the global bifurcation diagram of a three-parameter family of cubic Liénard
systems. This family seems to have a universal character in that its bifurcation diagram (or …

In this article, we present a new, geometric proof of known results for slow passage through
Hopf bifurcations (Baer et al.(1989), Neishtadt (1987, 1988), Shishkova (1973)). The new …

Abstract The Fisher–Kolmogorov–Petrowskii–Piscounov (FKPP) equation with cut-off was
introduced in (Brunet and Derrida 1997 Shift in the velocity of a front due to a cut-off Phys …

The cusp singularity—a point at which two curves of fold points meet—is a prototypical
example in Takens' classification of singularities in constrained equations, which also …

In this paper we prove finite cyclicity of several of the most generic graphics through a
nilpotent point of saddle or elliptic type of codimension 3 inside C∞ families of planar vector …