Dynamics of a Duopoly Model with Periodic Driving

We investigate a duopoly market describing the competition between two firms that produce goods of the same kind, under the assumption that their cost functions are proportional to the amounts produced. When the proportionality factor is constants it has been found that the model always leads to a stable equilibrium point. In this paper, we introduce cost functions that include periodic driving, which models fluctuations of prices that determine the production costs of a firm. In contrast to the undriven case, we find that the equilibrium point destabilizes and all solutions rapidly converge to a stable quasiperiodic attractor.