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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...

Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

Lin Lu, Yi Lian, Chaoling Li (2017)

Open Mathematics

This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.

Dynamics in a discrete predator-prey system with infected prey

Changjin Xu, Peiluan Li (2014)

Mathematica Bohemica

In this paper, a discrete version of continuous non-autonomous predator-prey model with infected prey is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions for the existence and global asymptotical stability of positive periodic solution of difference equations in consideration are established. An example shows the feasibility of the main results.

Dynamics of a two sex population with gestation period

Giorgio Busoni, Andrzej Palczewski (2000)

Applicationes Mathematicae

We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent')...

Dynamics of Nutrient-Phytoplankton Interaction in the Presence of Viral Infection and Periodic Nutrient Input

K. pada Das, S. Chatterjee, J. Chattopadhyay (2008)

Mathematical Modelling of Natural Phenomena

Chattopadhyay et al. [Biosystems (2003), 68, pp. 5-17] proposed and analyzed an N – P model in the presence of viral infection on phytoplankton population. They studied the dynamics under the constant nutrient input. The present paper deals with the problem with seasonal variability on nutrient input. We use a general periodic function for nutrient input. We observe the dynamics of the system by considering (i) the infected phytoplankton consumes nutrient and (ii) the infected phytoplankton is not...

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