The discretized or ultradiscretized model corresponds to some actual biological systems. Behavior as a discretized system is often essential to an ecological system.
Many species of plants and animals perform reproductive activity every year. The 3-Deazaneplanocin A dynamics can be described as a discrete system with δ=1 [year]. It is the common case that the production rate of species Y is enhanced by species X and conversely the species Y decrease the production rate of species X. Based on our research, we can conclude that this simple ecological negative feedback regulation can cause the oscillation as long as the condition (21) is satisfied. The number of population should be represented as a discrete value rather than continuous one when the distribution of individuals is sparse and the number of species is quite low. Ultradiscrete method should be applicable in this case.
AcknowledgmentWe would like to thank T. Kawabe (Kyushu University) for many helpful discussions. This research was supported by Inamori Foundation and Takeda Science Foundation (H.I.).