The Global Character of Solutions of an Anti-competitive System of Rational Difference Equations
DOI:
https://doi.org/10.5644/SJM.08.2.12Keywords:
Difference equations, competitive maps, anti-competitive maps, global asymptotic stability, period-2 solutionsAbstract
In this paper, we analyze the global character of the solutions of an anti-competitive system of rational difference equations. We
prove that the solutions of the system can have three different types of global behavior, corresponding to different regions of the parameter space. Our analysis utilizes a global convergence theorem from Camouzis and Ladas, and two theorems from Kulenovi´c and Merino that apply to competitive systems.
2000 Mathematics Subject Classification. 39A10, 39A11
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