Asymptotic behavior of solutions to second-order nonlinear differential equations.
Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system.
Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation.
Asymptotic position and shape of the limit cycle in a cardiac rheodynamic model.
Basic algebro-geometric conceps in the study of planar polynomial vector fields.
In this work we show that basic algebro-geometric concepts such as the concept of intersection multiplicity of projective curves at a point in the complex projective plane, are needed in the study of planar polynomial vector fields and in particular in summing up the information supplied by bifurcation diagrams of global families of polynomial systems. Algebro-geometric concepts are helpful in organizing and unifying in more intrinsic ways this information.
Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation
The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapunov quantities of the autonomous system associated with the modified Van der Pol-Mathieu equation are computed....
Bemerkung über die Form der Integrale der linearen Differentialgleichungen mit veränderlichen Coefficienten.
Bifurcation and total stability
Bifurcation diagram of a cubic three-parameter autonomous system.
Bifurcation of closed orbits from a limit cycle in
Bifurcation sequences in the dissipative systems with saddle equilibria
Bifurcations de polycycles infinis pour les champs de vecteurs polynomiaux du plan
Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.
It is proved in this paper that the maximum number of limit cycles of system⎧ dx/dt = y⎨⎩ dy/dt = kx - (k + 1)x2 + x3 + ε(α + βx + γx2)yis equal to two in the finite plane, where k > (11 + √33) / 4 , 0 < |ε| << 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.
Branching of periodic orbits from Kukles isochrones.
Canards et enlacements
Center conditions for a simple class of quintic systems.
Centering conditions for planar septic systems.
Centres and limit cycles for an extended Kukles system.
Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four
A class of degree four differential systems that have an invariant conic , , is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.
Commutators and linearizations of isochronous centers
We study isochronous centers of some classes of plane differential systems. We consider systems with constant angular speed, both with homogeneous and nonhomogenous nonlinearities. We show how to construct linearizations and first integrals of such systems, if a commutator is known. Commutators are found for some classes of systems. The results obtained are used to prove the isochronicity of some classes of centers, and to find first integrals for a class of Liénard equations with isochronous centers....