Noise with memory as a model of lemming cycles

Abstract

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. Examples of equations modeling population dynamics of lemmings (or their predators) 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. © 2008 Springer.