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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...

Dissipative systems

Crell, B. (1984)

Proceedings of the 12th Winter School on Abstract Analysis

Dynamic analysis of an impulsively controlled predator-prey system.

Baek, Hunki (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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

Pastravanu, Octavian, Voicu, Mihail (2003)

International Journal of Mathematics and Mathematical Sciences

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

Huo, Hai-Feng, Li, Wan-Tong (2006)

Discrete Dynamics in Nature and Society

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

Quang, Ta Hong, Ton, Ta Viet, Linh, Nguyen Thi Hoai (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Dynamics of a system of nonlinear differential equations.

Chumakov, G.A. (2007)

Sibirskij Matematicheskij Zhurnal

Dynamics of species in a nonautonomous Lotka-Volterra system.

Ton, Ta Viet (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Eighty fifth anniversary of birthday and scientific legacy of Professor Miloš Ráb

Ondřej Došlý, Eva Jansová, Josef Kalas (2014)

Archivum Mathematicum

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.

E. Wagenführer (1976/1977)

Numerische Mathematik

Energy decay estimates for Lienard's equation with quadratic viscous feedback.

Khapalov, Alexander Y., Nag, Parthasarathi (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Estimations of noncontinuable solutions of second order differential equations with $p$ -Laplacian

Eva Pekárková (2010)

Archivum Mathematicum

We study asymptotic properties of solutions for a system of second differential equations with $p$ -Laplacian. The main purpose is to investigate lower estimates of singular solutions of second order differential equations with $p$ -Laplacian ${(A (t) Φ_{p} (y^{'}))}^{'} + B (t) g (y^{'}) + R (t) f (y) = e (t)$ . Furthermore, we obtain results for a scalar equation.

Existence and sharp asymptotic behavior of positive decreasing solutions of a class [4pt] of differential systems with power-type nonlinearities

Jaroslav Jaroš, Kusano Takaŝi (2014)

Archivum Mathematicum

The system of nonlinear differential equations $x^{'} + p_{1} (t) x^{α_{1}} + q_{1} (t) y^{β_{1}} = 0, y^{'} + p_{2} (t) x^{α_{2}} + q_{2} (t) y^{β_{2}} = 0, A$ is under consideration, where $α_{i}$ and $β_{i}$ are positive constants and $p_{i} (t)$ and $q_{i} (t)$ are positive continuous functions on $[a, \infty)$ . There are three types of different asymptotic behavior at infinity of positive solutions $(x (t), y (t))$ of (). The aim of this paper is to establish criteria for the existence of solutions of these three types by means of fixed point techniques. Special emphasis is placed on those solutions with both components decreasing to zero as $t \to \infty$ , which can be...

Existence and uniqueness for the predator-prey model with diffusion in the scalar case.

Julián López-Gómez, Rosa Pardo (1991)

Extracta Mathematicae

We solve the problem of the existence and uniqueness of coexistence states for the classical predator-prey model of Lotka-Volterra with diffusion in the scalar case.