Affiliation:
1. Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881-0816, USA
Abstract
In this paper, certain dynamic scenarios for general competitive maps in the plane are presented and applied to some cases of second-order difference equation xn+1=fxn,xn−1, n=0,1,…, where f is decreasing in the variable xn and increasing in the variable xn−1. As a case study, we use the difference equation xn+1=xn−12/cxn−12+dxn+f, n=0,1,…, where the initial conditions x−1,x0≥0 and the parameters satisfy c,d,f>0. In this special case, we characterize completely the global dynamics of this equation by finding the basins of attraction of its equilibria and periodic solutions. We describe the global dynamics as a sequence of global transcritical or period-doubling bifurcations.
Cited by
3 articles.
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