The unforeseen mobile data explosion poses a major challenge to the performance of today’s cellular networks, and cellular networks are in urgent need of novel solutions to handle such voluminous mobile data. Obviously, data offloading through third-party Wi Fi access points(APs) can effectively alleviate the data load in the cellular networks with a low operational and capital expenditure. In this paper, we propose and analyze an adaptive Wi Fi-offloading algorithm based on attractor selection in heterogeneous wireless networks. In the proposed Wi Fi-offloading algorithm, the Wi Fi system throughput and cellular throughput in the coverage area of Wi Fi, are mapped into the activity of the attractor, which is the reflector of the current network environment. When the current attractor activity is low, the network is dominated by the noise. Then, the noise triggers the controller to select adaptive attractor, an optimal Wi Fi-offloading ratio φ, to adapt to the dynamic network environment. And users offload the specific portion of traffic to the Wi Fi networks with the ratio of φ, which improves the throughput of heterogeneous wireless networks and alleviates the load of cellular networks. Through simulation, we show that the proposed Wi Fi-offloading algorithm outperforms the existing ones with 21% higher heterogeneous network throughput in a dense traffic environment. The unforeseen mobile data explosion poses a major challenge to the performance of today’s cellular networks, and cellular networks are in urgent need of novel solutions to handle such voluminous mobile data. Obviously, data offloading through third-party Wi Fi access points (APs) can effectively alleviate the data load in the cellular networks with a low operational and capital expenditure. In this paper, we propose and analyze an adaptive Wi-offloading algorithm based on attractor selection in heterogeneous wireless networks. In the proposed Wi-off off algorithm, the Wi Fi system throughput and cellular throughput in the coverage area of ​​Wi Fi, are mapped into the activity of the attractor, which is the reflector of the current network environment. When the current attractor activity is low, the network is dominated by the noise Then, the noise triggers the controller to select adaptive attractor, an optimal Wi Fi-offloading ratio φ, to adapt to the dynamic network environm And users offload the specific portion of traffic to the Wi Fi networks with the ratio of φ, which improves the throughput of heterogeneous wireless networks and alleviates the load of cellular networks. Through simulation, we show that the proposed Wi Fi-offloading algorithm outperforms the existing ones with 21% higher heterogeneous network throughput in a dense traffic environment.