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Paper Information

Journal:   IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE   SUMMER 2014 , Volume 38 , Number A3; Page(s) 265 To 279.
 
Paper: 

DYNAMICS AND BIFURCATIONS OF A LOTKA-VOLTERRA POPULATION MODEL

 
 
Author(s):  KHOSHSIAR GHAZIANI R.*
 
* DEPARTMENT OF APPLIED MATHEMATICS, SHAHREKORD UNIVERSITY, SHAHREKORD, IRAN
 
Abstract: 

This paper investigates the dynamics and stability properties of a discrete-time Lotka-Volterra type system. We first analyze stability of the fixed points and the existence of local bifurcations. Our analysis shows the presence of rich variety of local bifurcations, namely, stablefixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate among afinite number of values; quasi-periodic cycles; which are constraint to stable attractor called invariant closed curve, and chaos, where population numbers change erratically. Our study is based on the numerical continuation method under variation of one and two parameters and computing different bifurcation curves of the system and its iterations. For the all codimension 1 and codimension 2 bifurcation points, we compute the corresponding normal form coefficients to reveal criticality of the corresponding bifurcations as well as to identify different bifurcation curves which emerge around the corresponding bifurcation point. In particular we compute a dense array of resonance Arnol'd tongue corresponding to quasi-periodic invariant circles rooted in weakly resonant Neimark-Sacker associated to multiplier l=e 2pqi with frequency q=2/5 We further perform numerical simulations to characterize qualitatively different dynamical behaviors within each regime of parameter space.

 
Keyword(s): NORMAL FORMS, STABLE CYCLES, CODIMENSION OF BIFURCATION, CENTER MANIFOLD
 
 
References: 
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Click to Cite.
APA: Copy

KHOSHSIAR GHAZIANI, R. (2014). DYNAMICS AND BIFURCATIONS OF A LOTKA-VOLTERRA POPULATION MODEL. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, 38(A3), 265-279. https://www.sid.ir/en/journal/ViewPaper.aspx?id=402761



Vancouver: Copy

KHOSHSIAR GHAZIANI R.. DYNAMICS AND BIFURCATIONS OF A LOTKA-VOLTERRA POPULATION MODEL. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE. 2014 [cited 2021May11];38(A3):265-279. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=402761



IEEE: Copy

KHOSHSIAR GHAZIANI, R., 2014. DYNAMICS AND BIFURCATIONS OF A LOTKA-VOLTERRA POPULATION MODEL. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, [online] 38(A3), pp.265-279. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=402761.



 
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