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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...

Differential stability of solutions to air quality control problems in urban area

Piotr Holnicki, Jan Sokołowski, Antoni Żochowski (1987)

Aplikace matematiky

The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.

Drift, draft and structure: some mathematical models of evolution

Alison M. Etheridge (2008)

Banach Center Publications

Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to classical...

Dynamic stability and spatial heterogeneityin the individualbased modelling of a lotkavolterra gas

Jacek Waniewski, Wojciech Jędruch, Norbert Żołek (2004)

International Journal of Applied Mathematics and Computer Science

Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the...

Dynamical behavior of Volterra model with mutual interference concerning IPM

Yujuan Zhang, Bing Liu, Lansun Chen (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...

Dynamical behavior of Volterra model with mutual interference concerning IPM

Yujuan Zhang, Bing Liu, Lansun Chen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...

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