A codimension two bifurcation with a third order Picard-Fuchs equation

On the algebraic solutions of the sixth Painlevé equation related to second order Picard-Fuchs equations

We describe two algebraic solutions of the sixth Painlevé equation which are related to (isomonodromic) deformations of Picard-Fuchs equations of order two. 1 Statement of the result In this note we describe two algebraic solutions of the following Painlevé VI ( PV I) equation dλ dt2 = 1 2 ( 1 λ + 1 λ− 1 + 1 λ− t )( dλ dt ) − ( 1 t + 1 t− 1 + 1 λ− t ) dλ dt + λ(λ− 1)(λ− t) t2(t2 − 1) [α + β t λ...

On a codimension two bifurcation for a class of second order ODEs

A Codimension-3 Bifurcation Problem

In this paper, a bifurcation phenomenon which arises from the interaction of static and dynamic modes in the vicinity of a compound critical point of a nonlinear autonomous system is considered. The critical point is characterized by a double zero and a pair of pure imaginary eigenvalues of the Jacobian. A set of simplified differential equations is obtained by applying the unification techniqu...

on a characteristic problem for a third order pseudoparabolic equation

in this paper, we investigate the goursat problem in the class c21(d)cn0 (d  p) c00 (d q)for a third order pseudoparabolic equation. some results are given concerning the existence and uniquenessfor the solution of the suggested problem.

Codimension two bifurcation observed in a phase converter circuit

Bifurcations observed in a phase converter circuit are investigated. We obtain a codimension two bifurcation which is intersection of period-doubling bifurcations. Periodic solutions generated by these bifurcations become chaotic states through a cascade of a codimension three bifurcation which is intersection of D-type of branching and period-doubling bifurcation.