This paper attempts to explore the dynamic relationship between new energy industry development and energy structure transformation in China. Based on the real option model and stochastic frontier analysis (SFA), the development scale and technical level of the new energy industry are measured at the provincial level. The eastern region is in the lead, but there has been a certain degree of technological efficiency retreat, especially in Liaoning. The new energy industry in the central region has developed rapidly due to the deepening of the industrialization process. With the aid of PVAR model, impulse response function and variance decomposition, the results show that there exists a bidirectional dynamic relationship between the new energy industry and energy structure. In other words, the development of the new energy industry and the energy transition can be mutually predicted. Specifically, technology effect has a positive continuous and dramatic influence on the transformation of energy structure. In turn, the energy transition first elicits a response to size effects, but has a long-term impact on technology effects. This implies that the new energy industry will usher in scale expansion at the early stage of energy transition. It is worth noting that scale expansion will not always accelerate the transition process. At that time, technology played a long-term and central role. Therefore, reasonable expansion of new energy industry scale and efforts to develop new energy technology are important measures to ensure the orderly energy transition.
The global bifurcations and chaotic dynamics of a thin-walled compressor blade for the resonant case of 2 : 1 internal resonance and primary resonance are investigated. With the aid of the normal theory, the desired form associated with a double zero and a pair of pure imaginary eigenvalues for the global perturbation method is obtained. Based on the simpler form, the method developed by Kovacic and Wiggins is used to find the existence of a Shilnikov-type homoclinic orbit. The results obtained here indicate that the orbit homoclinic to certain invariant sets for the resonance case which may lead to chaos in the sense of Smale horseshoes for the system. The chaotic motions of the rotating compressor blade are also found by using numerical simulation.
The multipulse homoclinic orbits and chaotic dynamics of a reinforced composite plate with the carbon nanotubes (CNTs) under combined in-plane and transverse excitations are studied in the case of 1 : 1 internal resonance. The method of multiple scales is adopted to derive the averaged equations. From the averaged equations, the normal form theory is applied to reduce the equations to a simpler normal form associated with a double zero and a pair of pure imaginary eigenvalues. The energy-phase method proposed by Haller and Wiggins is utilized to examine the global bifurcations and chaotic dynamics of the CNT-reinforced composite plate. The analytical results demonstrate that the multipulse Shilnikov-type homoclinic orbits and chaotic motions exist in the system. Homoclinic trees are constructed to illustrate the repeated bifurcations of multipulse solutions. In order to verify the theoretical results, numerical simulations are given to show the multipulse Shilnikov-type chaotic motions in the CNT-reinforced composite plate. The results obtained here imply that the motion is chaotic in the sense of the Smale horseshoes for the CNT-reinforced composite plate.
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