Аннотация:Population cycles in small rodents of the north are modeled by noise with memory. Multiannual
lemming density fluctuations are presented as a pulse sequence. These pulses correspond to the peaks of
lemming density. The memory is presented as some delay time after each pulse. During this time the next
pulse is forbidden. Parameter of periodicity, average period, correlation function and parameter of synchronization are calculated for different places of North America. The examples of equations modeling the lemming (or theirs predator) population dynamics are considered. The model of connected oscillators gives the qualitative explanation of synchronization effects and relation between synchronization and periodicity. These results have implication for the testing of hypotheses regarding lemming cycles.