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Based on the fact that the incubation periods of epidemic disease in asymptomatically infected and infected individuals are inevitable and different, we propose a diffusive susceptible, asymptomatically infected, symptomatically infected and vaccinated (SAIV) epidemic model with delays in this paper. To see whether epidemic disease can propagate spatially with a constant speed, we focus on the travelling wave solution for this model. When the basic reproduction number of the corresponding spatial-homogenous delayed differential system is greater than one and the wave speed is greater than or equal to the critical speed, we prove that this model admits nontrivial positive travelling wave solutions. Our theoretical results are of benefit to the prevention and control of epidemic.

In this paper, the semi-rational solutions that causes vector rogue waves and breathers can be obtained by using the Darboux dressing transformation. We studied vector rogue waves and the interaction between rogue waves and light-dark solitons, and observed that during the interaction, due to the interference between the light-dark components of the solitons, a respiration-like structures appears. Besides, it can be observed that the rogue waves and soliton merge together. Moreover, the main characteristics of the interactions between the breathers and bright-dark solitons are displayed with some graphics.

With the contradiction between supply and demand being intensified, the unreasonable crude oil trade structure has become increasingly prominent. Therefore, optimizing the supply and demand structure of the global crude oil trade is an urgent problem, which has become one of the crucial factors affecting the energy strategy and economic development of each country. This paper builds an optimization model that aims at minimizing crude oil trade costs based on the complex network theory. Meanwhile, an optimal solution generation approach is proposed and developed in this paper. Compared with the preoptimized trade network, the proposed model can effectively reduce the trade cost. By topological analysis of the trade network and its optimal configuration, we obtain that both the preoptimized and optimized crude oil trade networks follow power-law distribution. By using the minimum spanning tree, we find that the major crude oil net exporting countries have the most significant influence and are at the core in the optimized trade structure. This work focuses on the sustainable development of the global crude oil trade and provides a fresh perspective for the optimal crude oil trade system. Moreover, the methodology and model may be applied in the investigation of optimization for other energy system structures.

With the growing importance of bike-sharing systems, this paper designs a new framework to solve rebalancing problem. It contains two aspects: dynamic rebalancing within each station and static rebalancing among stations. Firstly, we give a new flow-type task window (F-window) by defining the consistency index of travelers. It is more suitable as a task window for rebalancing than time-type task window (T-window) based on three aspects analysis. Through three assumptions, the temporal-distribution learning model including task window and station storage configuration, are built to realize new dynamic rebalancing. The spatial-distribution learning method is introduced to divide management areas for static rebalancing. The empirical results show that F-window can better match the strong time-sensitive of demand fluctuation. Compared with traditional rebalancing needs hours, each rebalancing within a station can be completed within average 4 min. By setting the station storage configuration, it makes rebalancing in this paper meets the demand of 28.3 times the hourly rebalancing within one week. And the number of vehicles visiting stations has dropped below 20%.

In this paper, we investigate the existence and nonexistence of traveling wave solutions in a nonlocal dispersal epidemic model with spatio-temporal delay. It is shown that this model admits a nontrivial positive traveling wave solution when the basic reproduction number \begin{document}$ R_0>1 $\end{document} and the wave speed \begin{document}$ c\geq c^* $\end{document} ( \begin{document}$ c^* $\end{document} is the critical speed) and this model has no traveling wave solutions when \begin{document}$ R_0\leq1 $\end{document} or \begin{document}$ c . This indicates that \begin{document}$ c^* $\end{document} is the minimal wave speed.

In this paper, we study the time-fractional nonlinear Korteweg-de Vries (KdV) equation. By using the theory of semigroups, we prove the well-posedness of the time-fractional nonlinear KdV equation. Moreover, we present the boundary controllability result for the problem.

This paper analyzes the impact of climate damage function on the social cost of carbon (SCC) and the economic growth rate. In a two-sector economic model with endogenous growth, we construct a 7-dimensional nonlinear system and then linearize the nonlinear system to derive the expression of the SCC containing the damage function. We find that the selected damage function has significant impacts when we calculate the SCC. In our model, the long run SCC per unit of output is the discount flow of the damage function caused by temperature rise and it is also affected by temperature adjustment rate and some other parameters. The specific form of damage function directly affects the social evaluation of the externality of pollution. The concavity of the SCC in the time path depends on second derivative of the damage function in infinite time. Higher-order damage function increase the SCC. We find that when the society is in an optimal state, the long-term economic growth rate can still be guaranteed to be positive when the convex damage function is chosen. The key of mitigation and adaptation strategies is the development of effective climate policies. Thus, as global recommendations for mitigation and adaptation strategies, we recommendation policy makers to use a highly convex damage function to calculate the SCC. We suggest policy makers consider carbon tax policies based on SCC. This makes the economic view of pollution closer to the mitigation target of climate policy-makers.

This paper is concerned with traveling wave solutions in a discrete diffusion epidemic model with delayed transmission. Employing the way of contradictory discussions and the bilateral Laplace transform, we obtain the nonexistence of nontrivial positive bounded traveling wave solutions. Utilizing the super-/sub-solutions method and the fixed point theory, we derive the existence of nontrivial positive traveling wave solutions with both super-critical and critical speeds. Our results indicate that the critical speed is the minimal speed.

Rainfall erosivity (RE) is the ability of rainfall to cause soil or regolith erosion. Understanding the spatial distribution and temporal trends of RE is critical for assessing soil erosion risk and improving upon soil conservation planning. The aim of this paper is to study the temporal and spatial changes in RE in the Huaihe River Basin, China. This will be based on daily precipitation data from 67 meteorological stations in the Huaihe River Basin for the period 1971 to 2016. The assessment of the resulting RE values involved inverse distance-weighted (IDW) interpolation, Sen's slope estimation, and the Mann-Kendall nonparametric test. In addition, the possible influence of the El Nino – Southern Oscillation (ENSO) on RE in the Huaihe River Basin will be examined by the use of Cross Wavelet Transform (XWT) and Wavelet Coherence (WTC), where the relationship between RE and the multivariate ENSO index (MEI) are analyzed. The results showed that the spatial distribution of RE is characterized by it increasing from west to east and north to south. In most areas, the annual RE has increased slightly, while this upward trend in the southeastern part of the study area was more significant. The rainfall erosivity of rainstorms (RE-SM) in the Huaihe River Basin played a leading role in the annual RE, and 97% of the stations displayed the order of importance of the different categories of rainfall as rainfall erosivity of rainstorms (RE-SM) > rainfall erosivity of heavy rain (RE-HR) > rainfall erosivity of moderate rain (RE-MR). Over monthly time scales, the RE was the highest in July, while it was lowest in December, with the monthly differences being apparent. The RE in the Huaihe River Basin were relatively large during non-El Nino/La Nina periods and relatively small during El Nino/La Nina periods. Finally, correlations between RE and the MEI in various parts of the basin showed different characteristics over time and space, with both displaying similarities and differences.

The Liaodong Bay Subbasin (LDBS), Bohai Bay Basin, is one of the most petroliferous basins in China. The basin experienced a strong tectonic inversion in the Late Oligocene, which has been proven to have had a major influence on petroleum accumulation. However, the dynamic origin of this tectonic event is poorly understood. In this paper, we present a finite element-based dynamic modelling study of the Late Oligocene tectonic inversion in the basin based on geological, geophysical and geomorphological data with different boundary conditions. We compared the modelling results with actual geological data and concluded that the NE-SW-directed compression model (labelled with BC-1) is the preferred model, suggesting that the effects of the India-Eurasia collision were the main cause of the Late Oligocene tectonic inversion. The results suggested that the maximum horizontal principal compressive stress direction (σHmax) generally trends EN E-W SW in the whole basin. The majority of the basin features a strike-slip faulting stress regime; the normal fault regimes are limited to the major faults, and the thrust faulting regimes are present only in the northern area of the Liaodong Uplift and Liaozhong Depression. The predicted fault slip rates occurring along the LZ1 fault in the Liaozhong area are significantly higher than those in the Liaoxi and Liaodong areas. Two high shear strain rates belts are present along the major faults in the Liaoxi and Liaozhong areas, indicating that the major faults accommodated the majority of the strain rates. This tectonic inversion play a significant positive role in the accumulation of petroleum in the basin due to the favourable relationship among the high strain rates, the formation of inversion-related traps and the timing of hydrocarbon charging. The high strain rate belts are suggested as the preferred targets for oil and gas exploration.

This paper is concerned with a negative order modified Korteweg-de Vries (nmKdV) equation which is in the negative flow of the mKdV hierarchy. We construct the breather solutions by Hirota's bilinear method and derive the infinite conservation laws through the Lax pair of the nmKdV equation. By constructing a new Lyapunov function with the conservation laws, we obtain the nonlinear stability of the breather solutions.

We prove that positive solutions of an integral equation of Wolff type are radially symmetric and decreasing about some point in$R^{n}$. The hypotheses allow a wider range of exponents and are easier to apply than those in previous work.

In this paper, we present applications of the doubling lemma to nonlinear equations, including a k-Hessian equation and an integral equation of Wolff-type.

This paper focuses on a new method of converting multidimensional time series into complex networks. Compared with the previous studies, this method puts different variables into the same h...

As green behavior plays an increasingly important role today, in this paper, we aimed at investigating the spreading process of city resident green behavior. We applied classical threshold model and modified contagion model into a multiplex network to illustrate this dynamic process. Since people always act in conformity with the majorities when they make decisions or take actions, we consider the effects on negative individuals from their positive friends. Only when the proportion of centrist’s positive friends surpassed the local awareness ratio α , will he become positive. Also, we consider the influence from green awareness, which facilitate the green behavior. Last but not least, compulsory policy is also taken into account because it will force specific negative individuals to take such green behavior. The theoretical analysis is conducted by microscopic Markov chain approach and the numerical simulations are performed based on the Monte Carlo simulation. The results show that the intensity of policy regulation θ plays a vital role in both spreading threshold and final green behavior size. We attain a new explanation on the extinction of some behaviors and may provide advice on policy modification.

A nonlocal diffusion epidemic model with nonlocal delayed effects is investigated. The existence and non-existence of the non-trivial and non-negative traveling wave solutions for the model are obtained, respectively. It is found that the threshold dynamics of the model is determined by the basic reproduction number of the corresponding reaction system and minimal wave speed.

Carbon emission rights allocation affects the effective operation of carbon trading system, and then the achievement of energy saving and emissions reduction objectives. Reasonable allocation scheme should meet the principle of justice. Carbon emission rights allocation based on energy justice is a novel and worth discussing subject. This paper explores the optimization of carbon emission rights allocation based on energy justice. The justice-based model is built with the aid of Gini coefficient. The way to optimize allocation scheme with constraints of population, ecological productive land, fossil energy resources and GDP is discussed. Results show that fossil energy resources and ecological productive land play more important role in the allocation. The prime example is Inner Mongolia, its quota percentage change reaches up to 150.01%. As the GDP and population growth rate are fixed in a given interval, the quota allocation in eastern China shows some interesting results. When the GDP growth rate is 6.25%, the quotas of eastern China will not change with varying population growth rate. The allocation will enter a relative stable stage as the population growth rate is greater than or equal to 6.4‰. These results can provide China with experience to deal with the new problem appeared in carbon trading system like two-children policy and the new normal of economic growth.

This paper establishes a new endogenous growth model driven by green low-carbon behavior, optimizes the model and three systems with green low-carbon behavior in order to obtain the comprehensive effects of the empirical and policy of the three policies that have been set. This paper consists of three parts: green low-carbon behavior endogenous growth model, three green low-carbon behavior systems, empirical and policy effects. In the green low-carbon behavior endogenous growth model, we have built a new endogenous growth model, which is based on the existing endogenous growth model, considering the effects and influences of green low-carbon behavior. The model divides the economic system in green low-carbon behavior pattern into three modules: the production module, the household module and the R&D module. In the production module, we consider the number of knowledge diffusion in the intermediate goods and use the number of knowledge diffusion to explain the transmission of green low-carbon behavior. We consider environmental quality, capital, labor and emission input in the production function of the intermediate goods in a specific sector. Then we get the first-order conditions of intermediate producers based on the profit function of intermediate producers. In the household module, we consider consumption, environmental quality and carbon emissions in the representative household utility, and use Hamilton function in order to obtain the optimum conditions for the representative household with respect to consumption and physical capital. In the R&D module, we obtain the characteristics of the balanced growth path in a stable state. In the second part, we propose three green low-carbon behavior systems. Through the optimization of government budget, welfare function and the nine optimization solutions of the new model in green low-carbon behavior pattern, we compare the government’s green low-carbon behavior (GG), private green low-carbon behavior motivated by the government (PMG) and private green low-carbon behavior motivated by anarchy (PG). Finally, we draw the conclusion that PMG is an optimal system to achieve the highest growth rate and welfare level. In the part of empirical and policy effects, we propose three green low-carbon parameters that policymakers need to consider and then the numerical simulations are conducted based on data from the United States and China. Then we compare the results obtained from the two countries' numerical simulation, and get the comprehensive effects of green low-carbon behavior: growth welfare effect and knowledge diffusion effect.

The algorithm of limited penetrable horizontal visibility graphs (LPHVGs) including the limited penetrable horizontal visibility graph [LPHVG( ρ )], the directed limited penetrable horizontal visibility graph [DLPHVG( ρ )] and the image limited penetrable horizontal visibility graph [ILPHVG n ( ρ ) )] are used to map time series (or matrices) on graphs and are powerful tools for analyzing time series. We derive the degree distributions of LPHVGs using an iterative LPHVGs construction process. We propose a more intuitive method of reproducing the construction process of limited penetrable horizontal visibility graphs that is simple to calculate. We find that the results confirm the analytical results from previous methods. We then introduce the concept of sequential LPHVG( ρ ) motifs and present a theoretical way of computing the exact motif profiles associated with unrelated random series. We perform several numerical simulations to further check the accuracy of our theoretical results. Finally we use the analytical results of LPHVG( ρ ) motif profiles to distinguish among random, periodic, and chaotic signals and find that the frequency of the type-I motif captures sufficient information to easily distinguish among different processes.

We analysis the cascading failure of interdependent weighted networks based on percolation theory and local weighted flow redistribution rule. The weight of a node is B i θ , where B i is the betweenness of the node. We assume that the two networks A and B of size N A and N B are BA networks, and suppose two different one-to-one interdependent network, one is random, the other based on nodes’ betweenness. Assume that a failed node in network A leads to a redistribution of the flow passing through it to its neighboring nodes and the interdependent node in network B also to be disabled, where the two failure factors happen concurrently, or successively. We find that the one-to-one random interdependent weighted complex network reaches the strongest robustness level when the weight parameter θ =0.5, no matter cascading failure caused by two failure factors happen concurrently, or successively. And when the interdependent relationship based on nodes’ betweenness, θ =0.7 to get the strongest robustness level.

The inverse problem of finding the optimal network structure for a specific type of dynamical process stands out as one of the most challenging problems in network science. Focusing on the susceptible-infected-susceptible type of dynamics on annealed networks whose structures are fully characterized by the degree distribution, we develop an analytic framework to solve the inverse problem. We find that, for relatively low or high infection rates, the optimal degree distribution is unique, which consists of no more than two distinct nodal degrees. For intermediate infection rates, the optimal degree distribution is multitudinous and can have a broader support. We also find that, in general, the heterogeneity of the optimal networks decreases with the infection rate. A surprising phenomenon is the existence of a specific value of the infection rate for which any degree distribution would be optimal in generating maximum spreading prevalence. The analytic framework and the findings provide insights into the interplay between network structure and dynamical processes with practical implications.

This paper explores green development of Yangtze River Delta (YRD) under PREDS (Population-Resources-Environment-Development-Satisfaction) perspective. Based on gray relevance analysis, synergy evaluation model and factor analysis model are constructed with improvement of weight determination and relevance degree calculation. Synergy evaluation results show that for the entire YRD the relevance degree of green development increases strictly. As the synergistic effect of the inner system continues to rise, the green development tend toward equilibrium (2003–2017). The provincial level green development ranking is put forward. The results of factor analysis show that four dimensions' impacts on public satisfaction are different. The prediction of “13th Five-Year Plan” suggests that, improving environmental indicators is the most potential solution to promote green development of YRD. Investment completed in industrial pollution treatment is taken as an example to show how the index will affect satisfaction under different growth rates. It turns out that when the growth rate is below or over the critical value (16%), the influence will go out of the trough and continue to increase, forming a “J” curve.

PurposeThis paper aims to study the oscillation phenomenon before chaos as well as its mechanism of occurrence in the energy-saving and emission-reduction system.Design/methodology/approachThe system dynamics analysis, phase portrait analyses, equilibrium point analysis and bifurcation curve were applied to this paper.FindingsFirst, the authors find an oscillation phenomenon previous to chaos. Second, on the one hand, the existence of two unstable saddles is the reason for the occurrence of oscillation phenomenon. On the other hand, the increasing of carbon emissions can arouse oscillation phenomenon.Originality/valueThis paper finds an oscillation phenomenon previous to chaos in the energy-saving and emission-reduction system. The mechanism of occurrence of oscillation phenomenon is studied. The existence of two unstable saddles is the reason for the occurrence of such oscillation phenomenon. The oscillation is related with fold bifurcation. The study also provides a theoretical basis for the further study of chaos control.

Apart from the technical improvements, inducing the green citizen behavior is also a key way to reduce carbon emissions. Various studies have tried to identify the determinants of green behavior. Hitherto, there lacks a quantitative analysis directed to the effects of some factor on the outbreak of green behavior and the final adopted fraction. To fill this gap, this paper propose a Heterogeneous Green Behavior Spreading (HGBS) model to explore the impacts of negative information diffusion (about the green behavior) that effects on the spreading of green behavior. Simulations are performed on top of the two-layer multiplex networks, in which individuals are involved in two processes, the information diffusion in information layer and the green behavior spreading in physical contact layer. Based on the Microscopic Markov Chain Approach (MMCA) and the Monte Carlo (MC) simulations, we find the slight impact of information layer would make the green behavior harder to break out and reduce the adopted fraction. Moreover, the diversity of information diffusion ways makes it worse. It suggests that the control of negative information diffusion would be helpful in contributing to low-carbon city. Another effective way is to encourage individuals having more neighbours in real world to behave pro-environmentally since the adopted fraction is increased for small degree of the individuals in physical contact layer. It is essential to consider the heterogeneity in spreading activity if one wants to model the green behavior spreading.

According to the causal relationship among energy efficiency, energy price, and economic growth in China, a network structure of mutual transmission is constructed and a novel model of nonlinear dynamic system is also established. With the help of numerical simulation, the impacts of the parameters on the motion state of the system and the subsystem are analyzed. Then, the parameters are identified by means of BP neural network, and the model of novel dynamic system is given, which has a practical significance to reflect the actual situation of the system in China. According to the state of the actual evolution, we analyze the regulatory effect of the policy on the state of the system and find that four policies can all make the unstable system become stable. Comparing and analyzing the regulatory effects of the single and combined policy on the system show that the combined policy has a shorter time to reach the stable state and it is more conducive to the reduction of energy price. However, the single policy has a better effect on improving the level of energy efficiency and economic growth. In addition, the evolutionary paths of energy efficiency are analyzed at different regulatory levels under the same policy, and the results show that the higher the regulatory level is and the shorter time it takes to reach steady state for energy efficiency, the lower the level of energy efficiency is.

Detecting and characterizing community structure plays a crucial role in the study of networked systems. However, there is still a lack of understanding of how community structure affects the systems' resilience and stability. Here, we develop a framework to study the resilience of networks with community structure based on percolation theory. We find both analytically and numerically that the interlinks (connections between the communities) affect the percolation phase transition in a manner similar to an external field in a ferromagnetic-paramagnetic spin system. We also study the universality class by defining the analogous critical exponents $\delta$ and $\gamma$, and find that their values for various models and in real-world co-authors networks follow fundamental scaling relations as in physical phase transitions. The methodology and results presented here not only facilitate the study of resilience of networks but also brings a fresh perspective to the understanding of phase transitions under external fields., Comment: 15 pages,4 figures

The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable horizontal visibility graph associated with random series. We show that the random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution $P(k)\sim exp[-\lambda (k-2\rho-2)], \lambda = ln[(2\rho+3)/(2\rho+2)],\rho=0,1,2,...,k=2\rho+2,2\rho+3,...$, independent of the probability distribution from which the series was generated. We deduce the exact expressions of the mean degree and the clustering coefficient and demonstrate the long distance visibility property. Numerical simulations confirm the accuracy of our theoretical results. We then examine several deterministic chaotic series (a logistic map, the H$\acute{e}$non map, the Lorentz system, and an energy price chaotic system) and a real crude oil price series to test our results. The empirical results show that the limited penetrable horizontal visibility algorithm is direct, has a low computational cost when discriminating chaos from uncorrelated randomness, and is able to measure the global evolution characteristics of the real time series., Comment: 23 pages, 12 figures

Characterizing nonlinear time series using complex network science is a new multidisciplinary methodology. This paper puts forward a new time series prediction method based on data fluctuation network, named data fluctuation networks predictive model (DFNPM). The basic idea of the method is: first map time series into data fluctuation network and extract the fluctuation features of time series according to the topological structure of the networks, and then construct models with useful information extracted to predict time series. With Cushing, OK Crude Oil Future Contract 1 (Dollars per Barrel) and New York Harbor Regular Gasoline Future Contract 1 (Dollars per Gallon) as its sample data as well as DFNPM as its prediction model, the research makes a prediction on crude oil and gasoline futures prices from December 30, 2014 to February 26, 2015. A comparison is conducted between the result of the prediction and such traditional prediction models as grey prediction (GM) model, exponential smoothing model (ESM), autoregressive integrated moving average (ARIMA) model and radial basis function neural network (RBF) model, which shows that DFNPM performs significantly better than the above four traditional prediction models in both the direction and level of prediction.

The major goal of this paper is to focus on the co-movement between high-end talent and economic growth by a complex network approach. Firstly, the national high-end talent development efficiency from 1990 to 2015 is taken as the quantitative index to measure the development of high-end talent. The added values of the primary industry, secondary industry, tertiary industry are selected as economic growth indexes, and all the selected sample data are standardized by the mean value processing method. Secondly, let seven months as the length of the sliding window, and one month as the sliding step, then the grey correlation degrees between systems are measured using the slope correlation degrees, and the grey correlation degree sequence is mapped into the symbol series composed by three symbols { Y , O , N } based on the coarse graining method. Let three characters as a mode, the nodes are obtained by the modes according to the time sequence. Let the transformation between the modal be the edge, and the times of the transformation be weight, then the co-movement networks between national high-end talent development efficiency and the added values of the primary industry, secondary industry, tertiary industry are built respectively. Finally, the dynamic characteristics of the networks are analysed by the node strength, strength distribution, weighted clustering coefficient, conversion cycle of the modes and the transition between the co-movement modes. The results indicate that there are mutual influence and promotion relations between the national high-end talent development efficiency and the added values of the primary, secondary and tertiary industry.

In this article, we study the existence of pure multi-solitons for the quartic generalized Benjamin-Bona-Mahony (gBBM) equation. Motivated by Martel and Merle (2015,2010) [36,33] and El Dika and Martel (2004) [6], we prove the nonexistence of pure multi-solitons for this model. The main argument is the construction of an approximate solution for t ≫ 1, and the description of its asymptotics for x ≫ 1.

This paper explores the optimization scheme of carbon trading in China based on a novel energy-saving and emission-reduction (ESER) system with carbon price constraints. With the aid of nonlinear dynamics theory, the dynamics behavior of the novel system is discussed. Genetic algorithm and back propagation neural network is used to identify the quantitative coefficients according to the statistical data of the second period in European Union (EU). Taking the actual situation in EU for instance, the variables which are sensitive to carbon trading are detailedly researched. Enlightened by the EU’s experience, an optimal road of China’s carbon trading is put forward. The results show that carbon emissions could be controlled by carbon trading. The investment to carbon trading hampers economic growth in the near future, and ESER technical progress is negatively correlated with carbon trading in the long run. Demand and supply relationship is closely related to carbon price, both are the important issues in carbon trading system. Excessive government control and extortionate carbon price will deliver the opposite effect and even fatal influence on carbon trading system.

This paper attempts to explore the evolvement rule of energy-saving and emission-reduction with changing economic growth rate based on a novel energy-saving and emission-reduction system with multi-variable constraints. Energy structure adjustment, economic growth rate, new energy technology progress and other constrained variables are introduced into the novel system with the aid of nonlinear dynamics. The dynamic behavior of the new system is discussed by means of nonlinear dynamics theory. The quantitative coefficients of the actual system are identified based on the genetic algorithm-back propagation neural network. A scenario study of the actual system is carried out, and some valuable conclusions are presented. Energy structure adjustment is driven more by economic considerations according to China’s national conditions. Energy structure adjustment could perfectly control energy intensity, without obvious potential negative impact on economic growth. New energy technology progress has a better effect on controlling energy intensity, and the more mature the technology is, the better the effect is. Energy intensity is sensitive to economic growth rate. There is an optimal interval of economic growth rate, and energy intensity could be effectively controlled by adjusting corresponding constraint condition in this interval.

Consumer Price Index (CPI) is a comprehensive index which contains a large amount of market information. In order to effectively measure the running status of China’s consumer market and analyze the dynamic evolution characteristics of regional economic consumption in China, the eigenvalues and eigenvectors of random matrix are proposed to quantitatively describe the evolution relationship of provincial and regional CPI in China. Based on the provincial data of China’s CPI, system risk entropy, synchronicity ratio, stability and market induction are introduced to characterize the market evolution characteristics, and analyze the regional differences and synchronicity of the consumer price index of China and evaluate the development of China’s consumer market. The results show that the average system risk entropy of China’s consumer market for the period 2000–2015 is 0.1646, fluctuating in the range of 0.0512–0.3288, indicating a higher system risk of China’s consumer market. The system risk of China’s consumer market is still higher than the average in nearly 15 years. Fluctuating in the range of 0.3871–0.9355, the market synchronicity ratio has a mean of 0.7225, which reveals a higher market consistency level, a rising trend in fluctuation but an increasing tendency in the degree of unbalanced regional development. Evolution results of market induction demonstrate that the evolution of China’s consumer market has experienced four stages. The market induction has possessed a sustained growth trend since August 2010. Scenario analysis indicates that the key to effectively improve China’s consumer market system is to solve the lagging issue of China’s western region market on the basis of controlling and resolving of the existing risk.

This paper deals with existence problem of traveling wave solutions of a class of nonlinear Schrodinger equation having distributed delay with a strong generic kernal. By using the geometric singular perturbation theory and the Melnikov function method, we establish results of the existence of kink and anti-kink wave solutions of the nonlinear Schrodinger equation with time delay when the average delay is sufficiently small.

This paper is concerned with existence, uniqueness and asymptotic behavior of traveling wave fronts for a generalized Fisher equation with nonlocal delay. The existence of traveling wave fronts is established by linear chain trick and geometric singular perturbation theory. The strategy is to reformulate the problem as the existence of a heteroclinic connection in R 4 . The problem is then tackled by using Fenichel’s invariant manifold theory. The asymptotic behavior and uniqueness of traveling wave fronts are also obtained by using standard asymptotic theory and sliding method.

This paper is devoted to the optimal distributed control problem described by Camassa–Holm equation. We firstly investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary condition. By contrast with our previous result, the proof without considering viscous coefficient is a bigger improvement. Secondly, based on the well-posedness result, we find a unique optimal control for the controlled system with the quadratic cost functional. Moreover, by means of the optimal control theory, we establish the sufficient and necessary optimality condition of an optimal control, which is another major novelty of this paper. Finally, we also present the optimality conditions corresponding to two physical meaningful distributive observation cases and give an illustration about how to numerically apply the obtained results.

A silicon carbide (SiC) injection enhanced gate transistor with accumulation channel (AC-IEGT) is proposed in this letter, which has a barrier layer with small windows under the p+ shielding region. The new structure can enhance electron injection through accumulation channel. Thus, an optimized carrier density can be obtained in the emitter side. Compared with conventional SiC insulated gate bipolar transistor and carrier stored trench bipolar transistor, static simulation results show that the static characteristics of the device are improved significantly. The figure of merit ( $V_{\text {BR}}^{2}/R_{\text {on,sp}})$ of AC-IEGT increases by 81.96 % and 17.78 %, respectively. The mix-mode circuit simulation results show that the proposed could be more suitable for ultra-high voltage application.

In this paper, a directed and weighted world crude oil trade network is constructed. Based on the built network, we apply top network method and modified closed-system input-output method to assess the relative importance of countries in the international oil trade. The top 1 network consisting of top trade relations, can well reflect countries’ preference in choosing oil trade partners. As a simplified network model of international oil trade network, the top 1 network has been analyzed the structure and evolution. In order to identify important oil trading countries, the modified closed-system input-output analysis has yielded some promising results, which show countries who play key role in international oil trade, are trading large oil volumes. In addition, by describing the influences of countries on each other, we find major oil importers have a much effect on other countries, including major oil exporters. The evolution analysis obtained by these two methods coincide with each other. To conclude, some suggestions are given according to the results.

This work presents theoretical demonstration of two-dimensional electron gas (2DEG) at the interface between Al0.2Ga0.8N and 4H-SiC, based on the self-consistent solution of Schrödinger–Poisson equations. High sheet carrier density of 1.1×1013 cm-2 was obtained in the Al0.2Ga0.8N/4H-SiC heterostructure, which is comparable to the electron concentration in Al0.2Ga0.8N/GaN heterostructure. The current–voltage characteristics of a high-electron-mobility transistor (HEMT), based on the Al0.2Ga0.8N/4H-SiC heterostructure, show a saturated drain current of 1.5 A/mm at the gate voltage of 2 V and the transconductance of 194 mS/mm at -3.95 V. In spite of interface-roughness scattering and phonon scattering, the 2DEG at the AlxGa1-xN/4H-SiC interface exhibits high electron mobility values of 3365 cm2/ (V·s) at 77K and 1120 cm2/ (V·s) at 300K. These results indicate that AlxGa1-xN/4H-SiC heterostructure can significantly improve the mobility of SiC based power switching devices.

In this paper, we study the stability of modified Korteweg–de Vries equation breather. By using variable separation method, we obtain the exact breather-type soliton solutions. Moreover, this kind of solutions are globally stable in H2 topology, and we describe a simple, mathematical proof of the orbital stability and asymptotic stability of breather-type soliton solutions under a class of small perturbation.

This paper is concerned with the existence and asymptotic behavior of traveling wave fronts for a food-limited population model with spatio-temporal delay. Using geometric singular perturbation theory and Fredholm alternative, we establish the existence of traveling wave fronts of this model for sufficiently small time delay. The approach is to reformulate the problem as an existence question for a heteroclinic connection in \({\mathbb {R}}^6\). Furthermore, employing standard asymptotic theory, we obtain the asymptotic behavior of traveling wave fronts of this model for the first time.

Driven by Chinese government, China's natural gas power generation industry has to deal with the energy price's reformation, the price of natural gas, electric power and some other energy source will be made by market instead of government. In recent years, China's natural gas power generation industry has made an unprecedented progress in the development of improving the energy structure and promoting Green Economy greatly. By establishing the cost estimation model of natural gas power generation and using the method of analysis for sensitivity factor, we think that the prime cost of natural gas is high in aspect of energy source cost. However, from the point of view of carbon emission cost, the cost of natural gas power generation is lower than coal power generation. On the other side such as power generation equipment, most of constant costs has been spent on imported power generation equipment. Therefore, Chinese natural gas power generation industries should work together with the China government for reducing the price of natural gas, realizing the gas turbine home-made, establishing the natural gas storage system and finally stabilizing natural gas supply.

In this paper, a directed world crude oil trade network is constructed to learn the topological structure properties. We find the oil trade network follows power-law distribution. This is further confirmed by degree correlation coefficient, which implies the crude oil network is disassortative. The relationship of betweenness centrality value and node degree is analyzed. The result shows countries with high betweenness centrality, are also with high degree. In the whole sample time interval, the reciprocity value shows an increasing trend. A growing number of countries have expanded their bilateral trade relations. At last, some suggestions are given according to the results.

In this paper, we study the fractional Schrodinger equation \begin{equation*} (-\Delta)^{s} u+V(x)u=f(x,u), \quad x\in\mathbb{R}^{N}, \end{equation*} where $0< s

In this paper, we discuss two main problems. In the first section, we establish a new global distributed exact controllability of the periodic two-component $\mu\rho$-Hunter-Saxton system on the circle by means of a distributed control. And in the second section, we present corresponding result of the asymptotic stabilization problem about the periodic two-component $\mu\rho$-Hunter-Saxton system. By presenting concrete form of the feedback law, an equivalent system is got.

In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Backlund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

To better understand the characteristics of a bike-sharing system, we applied complex network methods to analyze the relationship between stations within the bike-sharing system. Firstly, using Gephi software, we constructed the public bicycle networks of different urban areas based on the real-time data of the Nanjing public bicycle system. Secondly, we analyzed and compared degree, strength, radiation distance, and community structure of the networks to understand the internal relations of the public bicycle system. The results showed that there were many stations with low usage of public bicycles. Furthermore, there was a geographical division between high-demand and low-demand areas for public bicycles. The usage of public bicycles at a station was not only related to land use but also related to the usage of bicycles at stations nearby. Moreover, the average service coverage of the public bicycle system was consistent with the original intention of &ldquo, the first and last mile&rdquo, and public bicycles could meet different travel needs.

Interdependent networks as an important structure of the real system not only include one-to-one dependency relationship but also include more realistic undirected multiple interdependent relationship. The study on interdependent networks plays an important role in designing more resilient real systems. Here, we mainly focus on the case of interdependent networks with a multiple-to-multiple correspondence of interdependent nodes by generalizing feedback and nonfeedback conditions. We develop a new mathematical framework and study numerically and analytically the percolation of interdependent networks with partial multiple-to-multiple dependency links by using percolation theory. By analyzing the process of cascading failure, the size of the giant component and the critical threshold are analytically obtained and testified by simulation results for couple Erdos-R e˙nyi and scale-free networks. The results imply that the system shows a discontinuous phase transition for different coupling strengths. We find that the system becomes more resilient and easy to defend by increasing the coupling strength and the connectivity density. Our model has the potential to shed light on designing more resilient real-world dependent systems.