Using discrete competition models where the density dependent growth functions are either all exponential or all rational, notwithstanding the complex interactions of the species, we establish an exclusion principle. Moreover, in a 2-species discrete competition model where the growth functions are exponential and rational, an example is given illustrating coexistence when our conditions are satisfied. We obtain an exclusion principle for this 2-species model for some choice of parameters.
A inathetnatical tiarnework is introduced to study attractors of discrete, nonatttonolnous dynamical systctns which depend periodically on time. A strttcture theorem for s~lch attractors is established which says that the attractor of a time-periodic dynainical system is the ~11tiix1 of attractors of appropriatc a~rtonontous {naps. If the nortautottornous systet~~ is a perturbntiort of an ailtottomoils map, properties that the t~onautono~uous attractor inherits 1.1-~III the autonotnous attractor are discussed. Examples I'ro~n population biology are preseittcd.
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