Open AccessGlobal Behavior of Four Competitive Rational Systems of Difference Equations in the Plane
Author(s) -
Mirela GarićDemirović,
M. R. S. Kulenović,
Mehmed Nurkanović
Publication year - 2009
Publication title -
discrete dynamics in nature and society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.264
H-Index - 39
eISSN - 1607-887X
pISSN - 1026-0226
DOI - 10.1155/2009/153058
Subject(s) - saddle point , plane (geometry) , mathematics , equilibrium point , saddle , stability theory , dynamics (music) , stability (learning theory) , mathematical analysis , mathematical economics , mathematical optimization , geometry , computer science , physics , differential equation , nonlinear system , quantum mechanics , machine learning , acoustics
We investigate the global dynamics of solutions of four distinct competitive rational systems of difference equations in the plane. We show that the basins of attractions of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or nonhyperbolic equilibrium points. Our results give complete answer to Open Problem 2 posed recently by Camouzis et al. (2009)
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom