Atmospheric carbon dioxide concentration [CO2], incoming solar radiation and sea ice coverage are among the most important factors that control the global climate. By applying the simple cell-to-cell mapping technique to a simplified atmosphere-ocean-sea ice feedback climate model, effects of these factors on the stability of the climatic system are studied. The current climatic system is found to be stable but highly nonlinear. The resiliency of stability increases with [CO2] to a summit when [CO2] reaches 290 (L/L which is comparable to the pre-industrial level, suggesting carbon dioxide is essential to the stability of the global climate. With [CO2] rising further, the global climate stability decreases, the mean ocean temperature goes up and the sea ice coverage shrinks in the polar region. When the incoming solar radiation is intensified, the ice coverage gradually diminishes, but the mean ocean temperature remains relatively constant. Overall, our analysis suggests that at the current levels of three external factors the stability of global climate is highly resilient. However, there exists a possibility of extreme states of climate, such as a snow-ball earth and an ice-free earth.