Dynamics of polynomial systems at infinity.
Dynamics of species in a nonautonomous Lotka-Volterra system.
Dynamics of systems with Preisach memory near equilibria
We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can also appear...
Dynamics of Tuberculosis: The effect of Direct Observation Therapy Strategy (DOTS) in Nigeria
This paper presents mathematical models for tuberculosis and its dynamics under the implementation of the direct observation therapy strategy (DOTS) in Nigeria. The models establish conditions for the eradication of tuberculosis in Nigeria based on the fraction of detected infectious individuals placed under DOTS for treatment. Both numerical and qualitative analysis of the models were carried out and the effect of the fraction of detected cases of active TB on the various epidemiological classes...
Ecuaciiones disipativas, conjuntos absorbentes y atractores
Effect of nonlinear perturbations on second order linear nonoscillatory differential equations.
Effect of randomly fluctuating environment on autotroph-herbivore model system.
Effect on persistence of intra-specific competition in competition models.
Effective computation of the first Lyapunov quantities for a planar differential equation
We take advantage of the complex structure to compute in a short way and without using any computer algebra system the Lyapunov quantities and for a general smooth planar system.
Eighty fifth anniversary of birthday and scientific legacy of Professor Miloš Ráb
The paper is concentrated on Professor Miloš Ráb and his contribution to the theory of oscillatory properties of solutions of second and third order linear differential equations, the theory of differential equations with complex coefficients and dynamical systems, and the theory of nonlinear second order differential equations. At the beginning, we take a brief look at the most important moments in his life. Afterwards, we describe his scientific activities on mentioned theories.
Ein Verfahren höherer Konvergenzordnung zur Berechnung des charakteristischen Exponenten der Mathieuschen Differentialgleichung.
Eine Bemerkung zu einem Satz von W. Hahn aus der Stabilitätstheorie linearer Systeme.
Energy decay estimates for Lienard's equation with quadratic viscous feedback.
Entrée-sortie dans un tourbillon
On étudie un champ de vecteurs lent-rapide de nommé tourbillon pour lequel on démontre l’existence d’une fonction entrée-sortie.
Entry into the sliding regime of solutions of nonautonomous operator equations.
Epidemiological Models and Lyapunov Functions
We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio...
Equilibrium stability of a servo actuating flight controls in a servoelastic framework.
Error estimation for perturbed systems.
estabilidad de órbitas relativistas
Estimates for Principal Lyapunov Exponents: A Survey
This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....