  Random walks serve as important tools for studying complex network
structures, yet their dynamics in cases where transition probabilities are not
static remain under explored and poorly understood. Here we study nonlinear
random walks that occur when transition probabilities depend on the state of
the system. We show that when these transition probabilities are non-monotonic,
i.e., are not uniformly biased towards the most densely or sparsely populated
nodes, but rather direct random walkers with more nuance, chaotic dynamics
emerge. Using multiple transition probability functions and a range of networks
with different connectivity properties, we demonstrate that this phenomenon is
generic. Thus, when such non-monotonic properties are key ingredients in
nonlinear transport applications complicated and unpredictable behaviors may
result.
