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Resource availability is a key component in animal ecology, yet the manner in which carnivore populations respond to spatial and temporal fluctuations of resources remains unclear. We take a population‐level approach to determine how resource pulses, in this case a temporary hyper‐abundance of prey, influence the densities and space‐use of cheetahs Acinonyx jubatus. The Maasai Mara in Kenya experiences an annual migration of > 1.4 million wildebeest Connochaetes taurinus and large numbers of zebras Equus quagga and Thomson's gazelle Eudorcas thomsonii thereby providing a natural experiment to examine the influence of resource pulses on carnivore movement and densities. To draw inferences on fluctuating cheetah densities and space‐use, we collected unstructured search‐encounter data during eight sampling sessions, four during and four out of the migration, and analysed these using Bayesian spatially‐explicit capture–recapture (SECR) models with sex‐specific detection function parameters. Both densities and space‐use fluctuated seasonally but this varied according to sex. Local cheetah densities increased in areas and during times when prey abundance was highest but this was more pronounced for females than males. In terms of space‐use, movements were larger during the migration than out of the migration but this was more pronounced for males than females. These results suggest that males are influenced more by resource distribution whereas females by resource abundance. Overall densities did vary but there was no clear pattern in relation to resource pulses. Understanding the behavioural drivers of population dynamics in relation to resource pulses can provide important insights into ecological processes at multiple ecological levels. [ABSTRACT FROM AUTHOR]