A simple model of the Arctic Ocean and Greenland Sea, coupled to a thermodynamic sea ice model and an atmospheric model, has been used to study decadal variability of the Arctic ice-ocean-atmosphere climate system. The motivating hypothesis is that the behavior of the modeled and ultimately the real climate system is auto-oscillatory with a quasi-decadal periodicity. This system oscillates between two circulation regimes: the Anticyclonic Circulation Regime (ACCR) and the Cyclonic Circulation Regime (CCR). The regimes are controlled by the atmospheric heat flux from the Greenland Sea and the freshwater flux from the Arctic Ocean. A switch regulating the intensity of the fluxes between the Arctic Ocean and Greenland Sea that depends on the interbasin gradient of dynamic height is implemented as a delay mechanism in the model. This mechanism allows the model system to accumulate the "perturbation" over several years. After the perturbation has been released, the system returns to its initial state. Solutions obtained from numerical simulations with seasonally varying forcing, for scenarios with high and low interaction between the regions, reproduced the major anomalies in the ocean thermohaline structure, sea ice volume, and freshwater fluxes attributed to the ACCR and CCR.