A discrete-time model for cryptic oscillations in predator–prey systems

We propose a model for the description of the so-called cryptic oscillations in predator–prey systems. Starting from a system of differential equations, we introduce a discretisation which allows us to numerically simulate the system and moreover, to derive a cellular automaton analogue based on the ultradiscretisation procedure. We extend our model so as to be able to describe, simultaneously, a transient regime of classical predator–prey oscillations and the cryptic regime, in which the predator population oscillates widely while the total prey population has only small-amplitude oscillations in phase opposition to those of the predator.