  Individual components of many real-world complex networks produce and
exchange resources among themselves. However, because the resource production
in such networks is almost always stochastic, fluctuations in the production
are unavoidable. In this paper, we study the effect of fluctuations on the
resource dependencies in complex networks. To this end, we consider a
modification of a threshold model of resource dependencies in networks that was
recently proposed, where each vertex has a fitness that depends on the total
amount of resource it has produced, the amount it has procured from its
neighbours, and the fitness threshold. We study how the ``network fitness'',
defined as the average fitness of vertices in the network, is affected as the
fluctuation size is varied. We show that the fluctuations worsen the network
fitness even when average production on vertices is kept fixed. This is true
independent of whether more than required amount is produced in the network or
not. However, this effect saturates for large fluctuations, and hence very
large fluctuations cannot worsen the network fitness beyond a limit. We further
show that the networks with a homogeneous degree distribution, such as the
Erdos-Renyi network, are less affected by fluctuations and also produce lower
wastage than the networks with a heterogeneous degree distribution like the
Scale-Free network. Our work shows that fluctuations in the resource production
should be avoided in resource dependency networks.
