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Global asymptotic behavior of a two-dimensional difference equation modelling competition

✍ Scribed by Dean Clark; M.R.S. Kulenović; James F. Selgrade

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
168 KB
Volume
52
Category
Article
ISSN
0362-546X

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✦ Synopsis

We investigate the global asymptotic behavior of solutions of the system of di erence equations xn+1 = xn a + cyn ; yn+1 = yn b + dxn ; n= 0; 1; : : : ;

where the parameters a and b are in (0; 1), c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. We show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior. In the case where a = b we ÿnd an explicit equation for the stable manifold.

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