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.
Degenerated singular cycles of inclination-flip type
Démonstration de quelques théorèmes sur les équations différentielles
Density of chaotic dynamics in periodically forced pendulum-type equations
We announce that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics for a dense set of forcing terms in a space of periodic functions with zero mean value. The approach is based on global variational methods.
Der verallgemeinerte Ljapunovsche Oszillationssatz
Determination of coupled sway, roll, and yaw motions of a floating body in regular waves.
Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model
An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103–112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling...
Devil's staircase route to chaos in a forced relaxation oscillator
We use one-dimensional techniques to characterize the Devil’s staircase route to chaos in a relaxation oscillator of the van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameter values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by Kennedy, Krieg and Chua (in [10]) related with the appearance of...
Die algebraische Struktur der allgemeinen Kummerschen Transformationen
Die Eindeutigkeit des Grenzzyklus bei der Liénardschen Differentialgleichung.
Die möglichen Wachstumsordnungen der Lösungen von linearen Differentialgleichungen.