Persistence and extinction of single population in a polluted environment.
Persistence of Crandall-Rabinowitz type bifurcations under small perturbations.
Perturbation of Hamiltonian Systems with Keplerian Potentials.
Perturbation singulière en dimension trois : canards en un point pseudo-singulier nœud
On étudie les systèmes différentiels singulièrement perturbés de dimension 3 du typeoù , , sont analytiques quelconques. Les travaux antérieurs étudiaient les points réguliers où la surface lente est transverse au champ rapide vertical. C’est le domaine d’application du théorème de Tikhonov. Dans d’autres travaux antérieurs, on étudiait les singularités de certains types : plis et fronces de la surface lente, ainsi que certaines singularités plus compliquées, analogues aux points tournants...
Perturbations of quadratic hamiltonian systems with symmetry
Phase and dispersion theory of the differential equation in connection with the generalized Floquet theory
Phase matrix of linear differential systems
Phase multistability of synchronous chaotic oscillations.
Phase portraits of planar vector fields: Computer proofs.
Phase synchronization in coupled Sprott chaotic systems presented by fractional differential equations.
Phasenraum-Methoden zum Studium nichtlinearer Differentialgleichungen.
Picone type formula for non-selfadjoint impulsive differential equations with discontinuous solutions.
Poincaré renormalized forms
Poincaré-Melnikov theory for n-dimensional diffeomorphisms
We consider perturbations of n-dimensional maps having homo-heteroclinic connections of compact normally hyperbolic invariant manifolds. We justify the applicability of the Poincaré-Melnikov method by following a geometric approach. Several examples are included.
Pointwise transformations of linear differential equations
Polynomial algebra of constants of the Lotka-Volterra system
Let k be a field of characteristic zero. We describe the kernel of any quadratic homogeneous derivation d:k[x,y,z] → k[x,y,z] of the form , called the Lotka-Volterra derivation, where A,B,C ∈ k.
Polynomial bounds for the oscillation of solutions of Fuchsian systems
We study the problem of placing effective upper bounds for the number of zeroes of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of Fuchsian systems of a given dimension having singular points. As a function of , this bound turns out to be double exponential in the precise sense explained in the paper.As a corollary, we obtain a solution of the so-called restricted infinitesimal...
Polynomial Riccati equations with algebraic solutions
We consider the equations of the form dy/dx = y²-P(x) where P are polynomials. We characterize the possible algebraic solutions and the class of equations having such solutions. We present formulas for first integrals of rational Riccati equations with an algebraic solution. We also present a relation between the problem of algebraic solutions and the theory of random matrices.
Polynomial systems: a lower bound for the weakened 16th Hilbert problem.
In this paper we provide the greatest lower bound about the number of (non-infinitesimal) limit cycles surrounding a unique singular point for a planar polynomial differential system of arbitrary degree.
Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population