Journals Information
Universal Journal of Applied Mathematics Vol. 2(4), pp. 161 - 169
DOI: 10.13189/ujam.2014.020401
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Discrete Time Stability Analysis of a Three Species Eco System
D.Ravi kiran 1,*, B.Rami reddy 2, N.Ch.Pattabhiramacharyulu 3
1 Department of Basic Science, Shri Vishnu Engineering College for Women, Bhimavaram 534202, India
2 Department of Mathematics, Hindu College, Guntur 522003, India
3 Former faculty, Department of mathematics, National Institute of Technology, Warangal 506002, India
ABSTRACT
In this paper, a three species eco system, involving three pairs is considered to examine the local asymptotic stability: A Prey-Predator, a Commensal-Host and an Ammensal-Enemy. Among the three species, one plays a dual role: A host and an enemy. Time is considered as a discrete unit and the system is modeled as a set of three difference equations. All the equilibrium states are identified and the local asymptotic stability of some of the equilibrium states is examined by considering the perturbation equations. It is observed that among the states, the state in which the Prey and its Host species are washed out(extinct), is spectrally stable and the state where the Predator/Ammensal species is washed out, is asymptotically stable. The results are illustrated with two dimensional plots as well as surface plots.
KEYWORDS
Prey, Predator, Ammensal, Commensal, Enemy, Host, Discrete Time, Asymptotic
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] D.Ravi kiran , B.Rami reddy , N.Ch.Pattabhiramacharyulu , "Discrete Time Stability Analysis of a Three Species Eco System," Universal Journal of Applied Mathematics, Vol. 2, No. 4, pp. 161 - 169, 2014. DOI: 10.13189/ujam.2014.020401.
(b). APA Format:
D.Ravi kiran , B.Rami reddy , N.Ch.Pattabhiramacharyulu (2014). Discrete Time Stability Analysis of a Three Species Eco System. Universal Journal of Applied Mathematics, 2(4), 161 - 169. DOI: 10.13189/ujam.2014.020401.