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The development and utilization of new energy is an important way to solve the energy shortage, environmental pollution and so on, which is also an effective power source for the development of low carbon economy. This paper starts with nonlinear dynamics, brings new energy into the dynamics system of energy-saving and emission-reduction and analyzes the effect of new energy on energy intensity and economic growth. Based on Lyapunov exponents and bifurcation diagrams, the dynamic behavior of the system is analyzed, energy-saving and emission-reduction attractor with new energy constraints is put forward. Artificial neural network is used to identify the quantitative coefficients in the simulation models according to the statistical data of China, and an empirical analysis of the real system is carried out with the results in perfect agreement with actual situation. The result shows that, by relying on the development of new energy or simply increasing investment to develop new energy, the effect of controlling energy intensity is not conspicuous. When the financial investment is too high, the inhibition effect on economic growth is great or fatal. Increasing overall investment in energy-saving and emission-reduction system which includes new energy, energy intensity could be declined better. When the overall investment gets larger, the inhibition effect on economic growth is also getting bigger in the early stage, however, with the further development of the dynamics system and the gradual maturity of new energy, the investment's promoting effect on economic growth is also very bigger. Numerical simulations are carried out to demonstrate the results. [ABSTRACT FROM AUTHOR]