D+-Stable Dynamical Systems on 2-Manifolds.
Dynamic bifurcation diagrams for some models in economics and biology.
Dynamical analysis of an interleaved single inductor TITO switching regulator.
Effective algebraic geometry and normal forms of reversible mappings.
We present a new method to compute normal forms, applied to the germs of reversible mappings. We translate the classification problem of these germs to the theory of ideals in the space of the coefficients of their jets. Integral factorization coupled with Gröbner basis constructionjs the key factor that makes the process efficient. We also show that a language with typed objects like AXIOM is very convenient to solve these kinds of problems.
Effective computation of the first Lyapunov quantities for a planar differential equation
We take advantage of the complex structure to compute in a short way and without using any computer algebra system the Lyapunov quantities and for a general smooth planar system.
Endogenous instability in credit-constrained emerging economies with Leontief technology.
Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions
Basic models suitable to explain the epidemiology of dengue fever have previously shown the possibility of deterministically chaotic attractors, which might explain the observed fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require strong enhanced infectivity on secondary infection, motivated by experimental findings of antibody-dependent-enhancement. Including temporary cross-immunity in such models, which is common knowledge among field researchers...
Equivariant Hopf bifurcation in a ring of identical cells with delay.
Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves
2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08.We obtain an upper bound for the number of zeros of the Abelian integral.The work was partially supported by contract No 15/09.05.2002 with the Shoumen University “K. Preslavski”, Shoumen, Bulgaria.
Examples of bifurcation of periodic solutions to variational inequalities in
A bifurcation problem for variational inequalities is studied, where is a closed convex cone in , , is a matrix, is a small perturbation, a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.
Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann
Existence and distribution of limit cycles in a Hamiltonian system.
Extended dynamical systems.
Feigenbaum numbers of certain flat-top families.
Final forms for a three-dimensional vector field under blowing-up
We study the final situations which may be obtained for a singular vector field by permissible blowing-ups of the ambient space (in dimension three). These situations are preserved by permissible blowing-ups and its structure is simple from the view-point of the integral branches. Technically, we take a logarithmic approach, by marking in each step the exceptional divisor of the transformation.
Finitely Determined Singularities of Formal Vector Fields.
Flows on supporting all links as orbits.
Flows with cyclic winding numbers groups.
Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems.
From the theorem of Ważewski to computer assisted proofs in dynamics