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This paper deals with a class of one element n-degree polynomial differential equations. By the fixed point theory, we obtain n periodic solutions of the equation. This paper generalizes some related conclusions of some papers.

In this paper, the Yangtze River Delta city group for the study, first, using data envelopment analysis estimates the energy efficiency of the city, and found that the Yangtze River Delta city group showing lower energy efficiency overall. Within the urban agglomeration 26 prefecture-level cities, Zhoushan is the only one achieving relatively effective energy efficiency. The spatial heterogeneity of energy efficiency in the urban agglomeration in the Yangtze River Delta is then measured using the Moran’s I index (including local), confirming the existence of low-energy efficiency clusters centered around Hefei and clusters of high-energy agglomeration centers centered around Hangzhou. Then the spatial error model is used to test the various factors that affect the energy efficiency of the urban agglomeration in the Yangtze River Delta based on the circumvention of spatial heterogeneity. The conclusion shows that there is a positive correlation between industrial structure, investment, scale, foreign trade and energy efficiency. Government influence and system is negatively related to energy efficiency. Finally, based on the conclusion, this paper puts forward the policy suggestion of promoting the energy efficiency of the urban agglomeration in the Yangtze River Delta.

Interactive innovation is the hotspot in the field of innovation. However, after consulting the information, it is found that the interaction innovation focuses on the interaction between the enterprise and the consumer and its effect. In this paper, 300 manufacturing enterprises in 15 sub-provincial cities were selected to conduct a questionnaire. We use the gray correlation to forecast manufacturing industry from 2016 to 2020 based on the total energy consumption and quantify the interactive innovation of manufacturing between enterprises and employees by Likert five-point scale. Using structural equation reveal the impact of interactive innovation on the production of energy-saving transformation. The conclusion shows that there are two types of innovation ,which are active and passive, and two kinds of interactive innovation can promote the transformation of production behavior, but neither of them has been paid attention. In addition, if the interactive innovation does not guide the policy properly, enterprises will enable to form a passive interactive innovation and inhibit the influence on initiative innovation.

In the process of urbanization, the rational project of urban scale is conducive to the improvement of electricity intensity, and the establishment of green cities and environment-friendly society. This paper selects the data of 13 prefecture-level cities in Jiangsu Province from 2005 to 2015, and establishes a dynamic panel model to conduct threshold regression analysis. The results show that there is an inverse U-shaped nonlinear relationship between the urban scale and the electricity intensity. In other words, as the urban scale expands, the electricity intensity increases firstly and then decreases. From the perspective of optimizing electricity intensity, this paper discusses the rational city scale under the optimal conditions of electricity intensity, and provides practical reference and decision support for the construction of a modern large-scale city during the process of urbanization in Jiangsu Province.

With the growth of economy, the impact of industrial transfer on carbon emissions gradually appears in the provinces. Employing the spatial econometric model and the data of provinces from 2006 to 2015, it is found that there is a significant correlation between industrial carbon emissions and the spatial distribution in China. The local space indicates the high concentration of carbon emissions includes Hebei, Inner Mongolia Liaoning, Jiangsu, Zhejiang, Shandong, Henan, Shanxi (Jin) and Shanxi (Shan) and so on. The industrial transfer in the developed regions deepens the spatial linkage between the economy and the carbon emissions in the provinces, so the spill over effect of carbon emissions gradually appears. This paper puts forward the addition of Inner Mongolia and Liaoning to the existing Beijing-Tianjin- Hebei regional linkage reduced efflux mechanism, adding Shandong to the existing Jiangsu - Zhejiang - Shanghai area linkage reduced efflux mechanism and starting the Henan-Shanxi-Shaanxi regional linkage emission reduction to prevent them from using the backward production and transferring the spill over effect cause by the industrial carbon emissions.

In the background of national energy administration conduct the research on electricity supply and demand equilibrium analysis, this paper forecast variation trend of Jiangsu province's electricity demand, structure and characteristic, combine the construction scale of planned electricity and external power, make the equilibrium analysis from the last year of twelfth-five to thirteen-five plan period. Results shows that Jiangsu province electricity demand growth slows down since industry structure adjustment, however, due to lack of energy resource, it still exist energy gap, specifically, 2017, 2020 has the gap of 18.9, 152.9,193 Billion Kw/h. Therefore, to ensure the demand of economic and society development, Jiangsu province need replenish certain electricity, and optimize the layout of electricity supply.

Based on the status quo of carbon emissions in USA and the international crude oil price fluctuations, this paper introduces control index and critical time of carbon emissions to find a new dynamic evolutionary model of carbon emissions of the States, deducing relative theories, such as Change Trends Theorem and Evolutionary Theorem. The critical time in the economic period is determined based on the evolutionary situation of the international crude oil price peaks, and it can be divided into four time intervals. Least-square method is used to analyze the dynamic evolutionary system of carbon emissions in the four time intervals with data provided by the international energy agency (IEA). Based on the nonlinear dynamic evolutionary model, the paper predicts carbon emissions by means of control index and control function, which facilitates carbon policy regulation and the system's external influence, and creates unique dynamic evolutionary factors of carbon emissions corresponding with the real situation of the United States. The financial crisis and shale gas large-scale mining have significantly changed America's energy supply structure. With the economy running upward, carbon emissions have a tendency to increase again. To achieve the goal of its reduction, different policies should be adopted by the US government. In this essay, the influence of the control index and the effect of critical time of carbon emissions to control function are analyzed. In addition, the dynamic evolutionary model is introduced and evolutionary scenario analysis is also conducted by modulating evolutionary coefficient and critical time.

Shell structure can help us understand the transport properties of the network clearly, and also identify the influential spreaders in complex networks. The robustness of networks suffering shell attacks is a topic of great interest since it is an important issue affecting many real-world networks. We study the robustness of two coupled network systems under shell attack, where multiple support-dependence relations are randomly built between nodes of networks. By using the general function of the degree distribution and taking Erdos-Renyi (ER) networks as an example, we numerically and analytically study the system robustness under shell attack to find the percolation threshold RA c . AS we remain the mean degree of networks k (k = k A = k B ) unchanged, let the k (a supplort degree of a node in one network, k = k A = k B ) decrease, RA c decreases too and the robustness of networks is reinforced. By exchanging the positions of k and k, we can get the similar conclusion. The results suggest that the robustness of the networks with multiple support-dependence links under shell attack relies not only on connectivity links of networks but also on support links.

With the help of the variable substitution and applying the fixed point theorem, we derive the sufficient conditions which guarantee the existence of the positive almost periodic solutions for a class of Lotka-Volterra type system. The main results improve and generalize the former corresponding results.

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter κ. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.

A new idea is put forward to modify the Clarkson–Kruskal (CK) direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the application of the modified CK direct method leads to three types of new similarity reductions different from the usual ones.

Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.

Using the tanh method and a variable separated ordinary difference equation method to solve the double sine-Gordon equation, we derive some new exact travelling wave solutions, especially a new type of noncontinuous solitary wave solutions. These noncontinuous solitary wave solutions are verified by using the conservation law theory.

The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the significant similarity reductions are obtained by virtue of the Lie group approach, and obtain abundant solutions of the coupled KdV equations, such as the solitary wave solution, exponential solution, rational solution, polynomial solution, etc.

In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg–de Vries (KdV) equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invariant solution of reduced equations can be acquired by means of the Painleve I transcendent function.

The existence of approximate inertial manifold using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation has a good localization property of the numerical solution distinguishably.

The traveling wave soliton solutions and pair soliton solution to a class of new completely integrable shallow water equation, Camassa-Holm equation are studied. The concept of concave or convex peaked soliton and smooth soliton were introduced. And the research shows that the traveling wave solution of that equation possesses concave and convex peaked soliton and smooth soliton solutions with the peakson. Simultaneously by applying Backlund transformation the new pair soliton solutions to this class of equation are given.

The existence of local attractors in thin 2D domains for the weakly damped forced KdV equation, whose principal operator is a non-self adjoint and non-sectorial one is given.

The time estimate of the blow-up of the weakly damped forced KdV equation in thin 2D domains is given.

The numerical analysis of the approximate inertial manifold in weakly damped forced KdV equation is given. The results of numerical analysis under five models is the same as that of nonlinear spectral analysis.

In the paper what is studied is the wild solution of the induced form under the spline wavelet basis in weakly damped forced KdV equation.