THEME SECTION: Fractional Dynamics and Control — PapersNo Access

CHAOS IN FRACTIONAL-ORDER POPULATION MODEL

IVO PETRÁŠ

Faculty of BERG, Technical University of Košice, Košice, 042 00, B. Němcovej 3, Slovak Republic

https://doi.org/10.1142/S0218127412500721Cited by:9 (Source: Crossref)

Abstract

This paper presents a fractional-order population model which consists of the two-predators and one-prey scheme. For this new model, the numerical solution is derived and the simulations are performed for various sets of model parameters together with stability analysis for commensurate and incomensurate orders of the fractional-order population model. The results obtained via the simulations show that chaos can be observed in such population model.

Keywords:

References

E. Ahmed, A. M. A. El-Sayed and H. A. A. El-Saka, J. Math. Anal. Appl. 325, 542 (2007). Crossref, Web of Science, Google Scholar
R. Caponetto et al. , Fractional Order Systems: Modeling and Control Applications ( World Scientific , Singapore , 2010 ) . Link, Google Scholar
Dorcákcaron;, L [1994] "Numerical models for the simulation of the fractional-order control systems," UEF-04-94, The Academy of Sciences, Inst. Experimental Physic, Kosice, Slovakia . Google Scholar
Ch. Jostet al., J. Anim. Ecol. 74, 809 (2005). Crossref, Web of Science, Google Scholar
A. Korobeinikov and G. C. Wake, J. Appl. Math. Decis. Sci. 3, 155 (1999). Crossref, Google Scholar
Ch. Li and Y. Wang, Comput. Math. Appl. 57, 1672 (2009). Crossref, Web of Science, Google Scholar
R. L. Magin , Fractional Calculus in Bioengineering ( Begell House Publishers , 2006 ) . Google Scholar
D. Matignon, Proc. Fract. Diff. Syst.: Models, Meth. App. 5, 145 (1998). Web of Science, Google Scholar
I. Petráš, Commun. Nonlin. Sci. Numer. Simulat. 15, 384 (2010). Crossref, Web of Science, Google Scholar
Petrás, I. [2010b] "Fractional order chaotic systems (Matlab toolbox)," MathWorks, Inc., Matlab Central File Exchange, url: www.mathworks.com/matlabcentral/fileexchange/27336 . Google Scholar
I. Petráš , Fractional-Order Nonlinear Systems , Springer Series on Nonlinear Physical Science ( 2011 ) . Crossref, Google Scholar
I. Podlubny , Fractional Differential Equations ( Academic Press , San Diego , 1999 ) . Google Scholar
I. Podlubnyet al., J. Comput. Phys. 228, 3137 (2009). Crossref, Web of Science, Google Scholar
N. Samardzija and L. D. Greller, Bull. Math. Biol. 50, 465 (1988). Crossref, Web of Science, Google Scholar
M. S. Tavazoei and M. Haeri, IET Sign. Proc. 1, 171 (2007). Crossref, Web of Science, Google Scholar
M. S. Tavazoei and M. Haeri, Phys. Lett. A 367, 102 (2007). Crossref, Web of Science, Google Scholar
M. S. Tavazoei and M. Haeri, Nonlin. Anal. 69, 1299 (2008). Crossref, Web of Science, Google Scholar
M. S. Tavazoei and M. Haeri, Physica D 237, 2628 (2008). Crossref, Web of Science, Google Scholar
Wikipedia [2010] "Lotka–Volterra equations," Wikimedia Foundation, Inc. (free encyclopedia) . Google Scholar