Received Revised

• Main Authors: N. Boccara, M. Roger
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 1999
• Subjects: Hudson; Hudson Bay; Lynx
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.8542; http://arxiv.org/pdf/adap-org/9904002v1.pdf

We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an “average probabilistic totalistic rule” exhibiting the same periodic behavior. Many natural populations of plants and animals exhibit large fluctuations of density with a roughly cyclic behavior. A well-known example is the oscillatory behavior of the Canadian lynx population as documented in the data compiled by the Hudson Bay Company over the period 1735-1940. Oscillations with an approximate period of about 10 years are observed with large amplitude fluctuations, which could, actually, correspond to a chaotic behavior. 1,2 Good introductions to population dynamics may be found in May 3 and Murray. 4 Most models in population dynamics are formulated in terms of differential equations or difference equations, which means that the local character of the interactions between prey and predators, for example, is not taken into account. In order to describe more correctly the local character of the predation process, it would be better to formulate predatorprey