1975 : A 2D predator-prey map

In 1975, John Rex Beddington, C. A. Free and John Lawton proposed a map governing two interacting populations, preys and predators : [1]

John Rex Beddington

where x_n designates the preys and y_n the predators. This two-dimensional discrete map considers populations with non-overlapping generations and was based on Nicholson-Bailey host-parasite equations to describe the interactions between a population of herbivorous arthropods --- invertebrate animal having an exoskeleton --- and their insect parasitoïds. [2] Beddington and coworkers observed some chaotic behaviors as the one plotted in Fig. 1 with the parameter values

This map is most likely one of the very first to be chaotic and published.

Fig. 1. Chaotic behavior produced by the 2D predator-prey map.