An eco-epidemiological model of competitive interacting species with Allee effect

An attempt has been made in the present investigation to extend and modify the study of the model representing competition of the species introduced by Gause (Science 79:16, 1934 ). His interesting piece of work has been updated here with the introduction of Allee effect in one species and the disea...

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Bibliographic Details
Published inInternational journal of dynamics and control Vol. 3; no. 3; pp. 239 - 252
Main Authors Rahman, Md. S., Chakravarty, Santabrata
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2015
Subjects
Complexity
Control
Control and Systems Theory
Dynamical Systems
Engineering
Vibration
Persistence
Eco-epidemiology
Global stability
Competition model
Allee effect
Boundedness
Multiple limit cycle
Local stability
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Summary:An attempt has been made in the present investigation to extend and modify the study of the model representing competition of the species introduced by Gause (Science 79:16, 1934 ). His interesting piece of work has been updated here with the introduction of Allee effect in one species and the disease in another species keeping the realistic biological situation in mind. The diseased population is classified into the susceptible and the infected categories. The equilibria of the model system under consideration has been analysed systematically in terms of the admittance of persistency, global stability together with the existence of Hopf bifurcation, bistability and the multiple limit cycles as well. Here center manifold theorem and normal form method are also used to find the nature of the bifurcating limit cycle. Numerical illustration has been finally carried out through graphical representations of those results towards the end in order to validate the applicability of the present model.
ISSN:2195-268X
2195-2698
DOI:10.1007/s40435-014-0114-5