Corrections to "Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas" (Dissertationes Math. 291 (1990))
Corrigendum to “On the boundedness and oscillation of solutions to .
Counting fixed points of a finitely generated subgroup of Aff [C].
Given a finitely generated subgroup G of the group of affine transformations acting on the complex line C, we are interested in the quotient Fix( G)/G. The purpose of this note is to establish when this quotient is finite and in this case its cardinality. We give an application to the qualitative study of polynomial planar vector fields at a neighborhood of a nilpotent singular point.
Covariant constructions in the theory of linear differential equations
Criteria for disfocality and disconjugacy for third order differential equations.
Criteria for oscillation of solutions of two-dimensional differential systems with deviating arguments.
Criteria of property for third order superlinear differential equations
Critical Point Theorems for Indefinite Functionals.
Croissance des solutions d'une équation différentielle homogène
Cubic and quartic planar differential systems with exact algebraic limit cycles.
Darbouxian integrability for polynomial vector fields on the 2-dimensional sphere.
Das Wachstum ganzer Lösungen gewisser linearer Funktional-Differentialgleichungen.
De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation
We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Prüfer transformation. We establish a de la Vallée Poussin type inequality for the distance of consecutive zeros of a nontrivial solution and this result we apply to the “classical” half-linear differential equation regarded as a perturbation of the half-linear Euler differential equation with the so-called critical oscillation constant. In the second part of the paper...
Decaying positive solutions of some quasilinear differential equations
The existence of decaying positive solutions in of the equations and displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. as ), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.
Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity
This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation , by means of regularly varying functions, where is a positive constant and is a positive continuous function on . It is shown that if is a regularly varying function, then it is possible to establish necessary and sufficient conditions for the existence of slowly varying solutions and regularly varying solutions of (A) which decrease to as and to acquire...
Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs
Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation...
Decomposition of homogeneous vector fields of degree one and representation of the flow
Decomposition solution for Duffing and Van der Pol oscillators.
Decoupling normalizing transformations and local stabilization of nonlinear systems
The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given.
Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system
In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.