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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...

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.

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 , ∞ ) . 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 → ∞ , which can be...

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