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Resource subsidies from external habitats can substantially affect the food web dynamics of local habitats. In this paper, we explore a mathematical model that is tailored for a stream food web, studied by Nakano and colleagues, in which consumers, in situ prey and subsidies all show seasonal fluctuation. The model reveals that the food web dynamics are stabilized if subsidies increase in summer when in situ productivity is low. Consumer dynamics are stabilized because subsidies complement seasonal resource deficiency. In situ prey dynamics are stabilized because subsidies indirectly balance the predation pressure by consumers, with seasonal change in prey carrying capacity. In summer when prey carrying capacity is low, seasonally abundant subsidies indirectly decrease predation pressure, whereas in winter, with high prey carrying capacity, scarce subsidies increase the predation pressure. Our results suggest that temporal productivity differences between spatially linked habitats are important to promote the stability of food web dynamics in a landscape context.