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.
Differential equations with infinite number of limit cycles
Differential growth models for microbial populations
Two models of microbial growth are derived as a resuslt of a discussion of the models of Monod and Hinshelwood types. The approach takes account of the lyse of dead cells in inhibitory products as well as in those which stimulate the growth. The asymptotic behaviour of the models is proved and the models applied to a chemostat.
Differential-algebraic equations in the theory of invariant manifolds for singular equations.
Diffusive synchronization of hyperchaotic Lorenz systems.
Disconjugacy and disfocality criteria for second order singular half-linear differential equations
We establish Vallée Poussin type disconjugacy and disfocality criteria for the half-linear second order differential equation , where α ∈ (0,1] and the functions are allowed to have singularities at the end points t = a, t = b of the interval under consideration.
Disconjugacy criteria for linear vector differential equations