Abstract
Even if the usual differential equations occurring in ecology show simple dynamical behavior, the corresponding equations modified by a time-delay mechanism or remodelled in a discrete version sometimes exhibit very complicated dynamics. For example, the dynamical behavior of a discrete prey-predator model in two dimensional system is considered. This model exhibits such complicated dynamical behavior as (1) a stable equilibrium point, (2) bifurcating cycles of period 2n (n=1, 2, ...), (3) Hopf-type bifurcations and subsequent bifurcations, (4) chaotic behavior.
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