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Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity

Ivana Kučerová (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation $x^{'''} + q (t) x^{- γ} = 0$ , by means of regularly varying functions, where $γ$ is a positive constant and $q$ is a positive continuous function on $[a, \infty)$ . It is shown that if $q$ 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 $0$ as $t \to \infty$ and to acquire...

Decoupling normalizing transformations and local stabilization of nonlinear systems

S. Nikitin (1996)

Mathematica Bohemica

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.

Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

P.S. Mandal, M. Banerjee (2012)

Mathematical Modelling of Natural Phenomena

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...

Displaying 1 – 10 of 10

Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity

Decoupling normalizing transformations and local stabilization of nonlinear systems

Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

Dissipative systems

Dynamic analysis of an impulsively controlled predator-prey system.

Dynamics of a class of uncertain nonlinear systems under flow-invariance constraints.

Dynamics of a nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional responses.

Dynamics of a non-autonomous three-dimensional population system.

Dynamics of a system of nonlinear differential equations.

Dynamics of species in a nonautonomous Lotka-Volterra system.

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