This paper examines the impacts of carbon tax on energy intensity and economic growth in a novel four-dimensional energy-saving and emission-reduction system with carbon tax constraints. Based on Lyapunov exponents and bifurcation diagrams, the dynamic behavior of the system is analyzed. The quantitative coefficients of the actual system are identified by artificial neural network. A scenario study is undertaken by observing the dynamic evolution behavior of energy intensity and economic growth in reality. The concept of turning point of energy intensity in the four-dimensional dynamic system is put forward for the first time. By adjusting the correlation coefficients of the four-dimensional system, more effective methods being performed to steadily and diligently reduce energy intensity. Take for instance the situation in China, the problem of when and how to introduce carbon tax are settled within the framework of the four-dimensional dynamic system. The results show that, as the tax levy point of carbon tax grows larger, the energy intensity of the four-dimensional system could be controlled better. It is both important and necessary to note the inhibition effect of these changes on economic growth. The best time to levy carbon tax and the best tax levy point are achieved after a comprehensive analysis within the framework of the four-dimensional dynamic system. The more appropriate time carbon tax is started, the higher growth rate of carbon tax is adopted, the better corresponding policies and laws are made, the easier the carbon emissions could be controlled and the more energy intensity could be declined, so as to achieve the goal of reducing the carbon dioxide emissions and keeping proper energy intensity. Numerical simulations are carried out to demonstrate the results. (C) 2013 Elsevier Ltd. All rights reserved.