Abstract

Coupling and coordination analyses of regional water resource systems (WRS) play an important role in promoting the sustainable and coordinated development of those systems. In this paper, a dynamic coupling coordination model is introduced to study the coordinated development of WRS. The weight of each index is obtained using an improved entropy weight method. The coupling and coordination degrees between resource subsystems and other subsystems and an entire system of water resources can be obtained using this model. Taking Heilongjiang, China, as an example, the results show that in 2005–2014, the WRS exhibited low coupling and low coordination characteristics due to a substantial contradiction between the resource subsystem and the social and economic and ecological subsystems. Therefore, strengthening the overall development of water resources, society, economy and ecology and improving the coupling abilities between resource subsystems and each of the other subsystems are effective strategies for promoting the coordinated development of WRS.

INTRODUCTION

Water resource systems (WRS) are composite systems that use resource subsystems as core carriers and ensure the coordinated development of societal, economic and ecological subsystems (Zhang & Wang 2014). Rapid population growth and economic development in many parts of the world has driven a concurrent increase in demand for water resources, which in turn has caused a deterioration of the ecological environment (Rusca et al. 2012). Therefore, it is of great practical importance to study and improve the coordination of relations between water resources and society, economy and ecology in WRS.

Some scholars have studied the coordinated development of WRS from the perspective of resources. Cheng et al. (2015a) combined water and land resources and used complex adaptive system (CAS) theory to study the sustainable development of regional water resources and social economy, and the authors also defined a coordinated development plan for water resources from the perspective of food security (Cheng et al. 2015b). Ren et al. (2016) promoted the coordinated development of regional water resources and social economy by using metabolic theory to address the problems of water shortage and the uneven spatial and temporal distributions of water resources. These studies lack a description of the overall coordinated development process between water resources and social economy.

Most scholars have studied the coordinated development of WRS in terms of factors such as climate, environment or natural disasters. Fowler et al. (2000) proposed a plan for the coordinated development of WRS by simulating potential atmospheric circulation changes. Hamouda et al. (2009) studied the coordination of WRS from the framework of a vulnerability assessment of WRS. Yan et al. (2014) studied a quantitative evaluation method of the coordinated development of WRS for the Dongliao River basin which has a high frequency of drought. Tseng et al. (2015) analysed the short-term effect of water shortage on the coordinated development of Taiwan water resources system through a drought evaluation index. Whateley et al. (2016) used the sequent peak algorithm and a hydrological model to study the effects of climate change on the coordinated development of WRS. The above studies mainly focus on the coordination of WRS according to specific factors and limited assumptions.

Some studies have also emphasized the coordinated development of WRS in view of specific characteristics of WRS. Liu et al. (2012) proposed a quantitative method for estimating the resilience of WRS in accordance with the law of possible transfer between different phases of water resources in adaptive periods. According to the characteristics of conflict of interest and diversity in water resources management, Giuliani & Castelletti (2013) proposed a new decision analysis model for multi-agent systems to study coordination and cooperation among different decision makers. These studies mainly focus on the regularity of water resources under specific conditions.

In summary, there is a lack of research on the coordinated development of WRS from a systems point of view with a comprehensive consideration of water resources, society, economy and ecology. Therefore, considering the dynamic characteristics of the interaction between water resources, society, economy and ecology, a new dynamic coupling and coordination model is proposed in this paper. In this model, coupling degree is used to describe the degree of interaction between elements within a system or subsystem, coordination degree is used to measure the degree of consistency of the coordinated development between the elements within a system or subsystem, and the dynamic and coordinated development process of WRS is studied by combining the two abovementioned degrees, which provides a reference for decisions regarding the coordinated development of regional WRS.

STUDY AREA

Heilongjiang Province is located in north-eastern China; it is China's largest commodity grain production base. Its geographical coordinates are 121°11′-135°05′E longitude and 45°25′-53°33′N latitude (see Figure 1). The land area of Heilongjiang Province is about 4.73 × 105 m3, accounting for around 5% of the total land area of China. The average annual consumption of agricultural and industrial water is approximately 2.19 × 108 m3 and 5.61 × 107 m3 respectively. However, the annual economic ratio of agricultural to industrial unit water (output value/water consumption) is 6:11, indicating that there is a serious disharmony in the water resource system. Additionally, compared to the national agricultural industrial water ratio (3:1), the utilization of agricultural water in Heilongjiang is higher than the national average for China. The above phenomenon seriously affects the sustainable development of WRS in the region (Ma 2013).

Figure 1

Location of the study area.

Figure 1

Location of the study area.

RESEARCH METHODS

Establishment of the index system

According to the ‘International Water Management Standards for the Promotion of Sustainable Use of Freshwater’ issued by the Global Water Management Partnership (GWP) and the ‘Annual Report on Water Resources Management’ issued by the Water Resources Department of the Ministry of Water Resources in China, and based on the principles of being objective, systematic, dynamic, data-focused and attentive to regional characteristics, an index system was established that incorporates resource, societal, economic and ecological perspectives (see Table 1).

Table 1

Evaluation index system of the coordinated development of WRS

IndexEquation (units)Meaning of the index
Resource subsystem 
 Utilization ratio of water resources (C1) (−) Water resource development use amount/total water resources (%) Degree of water resource consumption 
 Modulus of water supply (C2) (−) Output of water supply /total land area (104 m3/km2Degree of water consumption per unit land area 
 Water resources per unit area (C3) (+) Local water resource amount/total land area (104 m3/km2Degree of abundance or lack of water resources 
 Natural water resource amount (C4) (+) Rainfall, runoff, snow and other natural resources (104 m3Water resource regulation ability 
 Utilization ratio of surface water resources (C5) (−) Surface water resource utilization amount/surface water resource amount (%) Consumption degree of surface water resources 
 Utilization ratio of groundwater resources (C6) (−) Groundwater resource utilization amount/groundwater resource amount (%) Consumption degree of groundwater resources 
Social subsystem 
 Population density (C7) (−) Total population/total land area (persons/km2Coordinated development level of society and water resources 
 Urbanization rate (C8) (−) Urban population/total population (%) Condition of social development 
 Per capita domestic water consumption (C9) (+) Regional total water consumption/total population (m3/person) Level of water demand for society 
 Per capita water resources (C10) (+) Amount of regional water resources/total population (m3/person) Supply ability of water to society 
Economic subsystem 
 GDP per capita (C11) (−) Regional GDP total/total population (104CNY/person) Coordinated development level of economy and water resources 
 Proportion of primary industry (C12) (−) GDP of the primary industry/total GDP (%) Regional economic structure 
 Water consumption per unit irrigated area (C13) (−) Agricultural water consumption/effective irrigation area (m3/hm2Water consumption intensity of farmland irrigation 
 Million Yuan industrial output water consumption (C14) (−) Industrial water consumption/gross industrial production (104 CNY m−3Industrial water consumption intensity 
 Grain yield per unit water consumption (C15) (+) Grain yield/agricultural water consumption (kg/m3Usage level of agricultural water 
Ecological subsystem 
 Environmental water use rate (C16) (−) Eco-environmental water consumption/total regional water resources (%) Coordinated development level of ecology and water resources 
 Forest coverage rate (C17) (+) Forestry area/total land area (%) Natural water storage capacity 
 Compliance rate of industrial wastewater discharge (C18) (+) Discharge of industrial waste water to meet discharge requirements/total industrial wastewater discharge (%) Ability to control environmental degradation 
 Soil erosion rate (C19) (−) Soil erosion area/total land area (%) Reflection of the influences of flood and drought 
IndexEquation (units)Meaning of the index
Resource subsystem 
 Utilization ratio of water resources (C1) (−) Water resource development use amount/total water resources (%) Degree of water resource consumption 
 Modulus of water supply (C2) (−) Output of water supply /total land area (104 m3/km2Degree of water consumption per unit land area 
 Water resources per unit area (C3) (+) Local water resource amount/total land area (104 m3/km2Degree of abundance or lack of water resources 
 Natural water resource amount (C4) (+) Rainfall, runoff, snow and other natural resources (104 m3Water resource regulation ability 
 Utilization ratio of surface water resources (C5) (−) Surface water resource utilization amount/surface water resource amount (%) Consumption degree of surface water resources 
 Utilization ratio of groundwater resources (C6) (−) Groundwater resource utilization amount/groundwater resource amount (%) Consumption degree of groundwater resources 
Social subsystem 
 Population density (C7) (−) Total population/total land area (persons/km2Coordinated development level of society and water resources 
 Urbanization rate (C8) (−) Urban population/total population (%) Condition of social development 
 Per capita domestic water consumption (C9) (+) Regional total water consumption/total population (m3/person) Level of water demand for society 
 Per capita water resources (C10) (+) Amount of regional water resources/total population (m3/person) Supply ability of water to society 
Economic subsystem 
 GDP per capita (C11) (−) Regional GDP total/total population (104CNY/person) Coordinated development level of economy and water resources 
 Proportion of primary industry (C12) (−) GDP of the primary industry/total GDP (%) Regional economic structure 
 Water consumption per unit irrigated area (C13) (−) Agricultural water consumption/effective irrigation area (m3/hm2Water consumption intensity of farmland irrigation 
 Million Yuan industrial output water consumption (C14) (−) Industrial water consumption/gross industrial production (104 CNY m−3Industrial water consumption intensity 
 Grain yield per unit water consumption (C15) (+) Grain yield/agricultural water consumption (kg/m3Usage level of agricultural water 
Ecological subsystem 
 Environmental water use rate (C16) (−) Eco-environmental water consumption/total regional water resources (%) Coordinated development level of ecology and water resources 
 Forest coverage rate (C17) (+) Forestry area/total land area (%) Natural water storage capacity 
 Compliance rate of industrial wastewater discharge (C18) (+) Discharge of industrial waste water to meet discharge requirements/total industrial wastewater discharge (%) Ability to control environmental degradation 
 Soil erosion rate (C19) (−) Soil erosion area/total land area (%) Reflection of the influences of flood and drought 

Note: ‘(+)’ represents a positive index; it indicates that the larger is the index value, the better is the coordinated development of the system. ‘(−)’ represents a negative index; it indicates that the smaller is the target value, the better is the coordinated development of the system.

Determination of index weight

When using the traditional entropy weight method to determine index weight, an effective description of interactions between indicators of WRS is lacking. The index weight obtained using this method is greatly affected by different coefficients, particularly in the case of a weight of 0; thus, this paper introduces the index sample standard deviation to improve the traditional entropy weight method. The calculation steps are as follows:

Step 1: Normalize the information of the individuals

Assume that the sample set is , where denotes the index of the sample, and m and n denote the number of indexes and the sample size, respectively. The specific process of the index is shown as Equation (1). 
formula
(1)
where and indicate the maxima and the minima, respectively, of the index of the sample.

Step 2: Calculate the entropy value of each index

Assume that is the entropy value of the evaluation index, and n is the number of evaluation objects. The entropy information can be calculated as follows: 
formula
(2)
where 
formula
Step 3: Calculate the weight of each index 
formula
(3)
where is the improved entropy weight of the evaluation index, and m is the number of indexes.

Dynamic coupling coordination model of WRS

The interactions between the subsystems of a water resource system are a nonlinear process. This study applies the idea of systematic evolution to establish the evolution equations of each subsystem: 
formula
(4)
where i is the number of indicators of each subsystem, and f is a nonlinear function of .

Because the stability of a nonlinear system is mainly determined by the characteristics of the root function, we can expand Equation (4) at as a Taylor series expansion, given the stability of the system. By omitting the higher-order terms , a linear function of the system can be approximated as . The evolution functions for the resource subsystem, social subsystem, economic subsystem and ecological subsystem can be expressed as follows:

 
formula
(5)
where r, x, y, and z represent the elements of the resource, social, economic and ecological subsystems, respectively, and , , , and are their respective weights. It is worth noting that, based on the given sample data, only discrete points satisfying the evolution equation can be obtained; therefore, we need to fit the discrete points. In this study, the evolution equations and fitting curves of each subsystem were obtained using the cftool toolbox in MATLAB.
Given the complex relationship between the resource subsystem and each of the other subsystems, we transform the two systems into one comprehensive system. According to the system structure, the evolution functions can be written as follows: 
formula
(6)
where A and B represent the dynamic evolution trend of the resource subsystem and each other subsystem, respectively, and and are the evolution speeds under various conditions for the two subsystems.
The angle between and represents the coupling degree of the two systems, and satisfies such that ; upon converting angle to radians, the specific equation is as follows: 
formula
(7)
The coupling degree can reflect only interaction intensity and cannot reflect the direction or pros and cons of the interaction, whereas the coordination degree can reflect the degree of coordination of the system and the degree of disorder to the order of the system (Ma et al. 2016). Thus, this paper introduces the coordination degree . The specific equation is as follows: 
formula
(8)
where , , and represent the comprehensive evaluation functions of the resource, social, economic and ecological subsystems, respectively; , , and represent the weights of each subsystem; , , and represent the normalized values of each subsystem, respectively, used to quantitatively determine the two-system coordination at the same time as the comprehensive coordination index T is introduced; and represents the undetermined coefficients of any two evaluation functions, the values of which should be (Ma et al. 2016).
According to the coupling degree between subsystems, the coupling degree of the water resource system is obtained by using the capacity coupling coefficient model in physics (Illingworth 1996), and the coordination degree of the system is obtained via C and the comprehensive coordination index . The specific equation is as follows: 
formula
(9)
where a, b, c and d are the undetermined coefficients of the subsystems, the values of which should be , and (Zhang & Su 2015).

Grade division of the coordinated development of WRS

According to the coupling degree and coordination degree, the grade of the coordinated development of water resources is divided using the median segmentation method (Li et al. 2012a; Wang et al. 2015) as shown in Table 2.

Table 2

Grade division of the coordinated development of WRS

Coupling degree level
Coordination degree level
GradeGrade intervalMeaningGradeGrade intervalMeaning
(0, 0.3] The system is in a low coupling stage. (0, 0.2] The system is in a recession stage. 
II (0.3, 0.5] The system is in an antagonistic stage. II (0.2, 0.4] The system is in a barely coordinated stage. 
III (0.5, 0.8] The system is in a running-in stage. III (0.4, 0.8] The system is in a moderately coordinated stage. 
IV (0.8, 1] The system is in a high coupling stage. IV (0.8, 1] The system is in a well-coordinated stage. 
Coupling degree level
Coordination degree level
GradeGrade intervalMeaningGradeGrade intervalMeaning
(0, 0.3] The system is in a low coupling stage. (0, 0.2] The system is in a recession stage. 
II (0.3, 0.5] The system is in an antagonistic stage. II (0.2, 0.4] The system is in a barely coordinated stage. 
III (0.5, 0.8] The system is in a running-in stage. III (0.4, 0.8] The system is in a moderately coordinated stage. 
IV (0.8, 1] The system is in a high coupling stage. IV (0.8, 1] The system is in a well-coordinated stage. 

Data sources

The initial data for the water resource system evaluation index system were obtained from the Heilongjiang Statistical Yearbook (2005–2014), the Heilongjiang Agricultural Yearbook (2005–2014), the China Statistical Yearbook (2005–2014) and a field study conducted during this research project.

RESULTS

The coupling and coordination degrees of the study area's water resource system and between the resource subsystem and each of the other subsystems in 2005–2014 can be obtained by the dynamic coupling coordination model (see Table 3). Figure 2 shows the variation of coupling and coordination degrees during the study period.

Table 3

Coupling degree and coordination degree of the water resource system (2005–2014)

Year2005200620072008200920102011201220132014
R-S Coupling degree 0.500 0.766 0.586 0.676 0.962 0.689 0.503 0.501 0.507 0.500 
Coordination degree 0.299 0.353 0.254 0.246 0.395 0.280 0.212 0.229 0.273 0.251 
R-J Coupling degree 0.464 0.713 0.926 0.784 0.966 0.814 0.509 0.908 0.508 0.984 
Coordination degree 0.278 0.329 0.331 0.304 0.388 0.366 0.271 0.338 0.301 0.368 
R-E Coupling degree 0.966 0.760 0.968 0.721 0.541 0.884 0.923 0.509 0.956 0.971 
Coordination degree 0.399 0.329 0.264 0.247 0.274 0.343 0.343 0.279 0.431 0.364 
WRS Coupling degree 0.315 0.333 0.325 0.333 0.322 0.332 0.320 0.320 0.318 0.318 
Coordination degree 0.225 0.220 0.179 0.182 0.218 0.214 0.200 0.205 0.231 0.204 
Year2005200620072008200920102011201220132014
R-S Coupling degree 0.500 0.766 0.586 0.676 0.962 0.689 0.503 0.501 0.507 0.500 
Coordination degree 0.299 0.353 0.254 0.246 0.395 0.280 0.212 0.229 0.273 0.251 
R-J Coupling degree 0.464 0.713 0.926 0.784 0.966 0.814 0.509 0.908 0.508 0.984 
Coordination degree 0.278 0.329 0.331 0.304 0.388 0.366 0.271 0.338 0.301 0.368 
R-E Coupling degree 0.966 0.760 0.968 0.721 0.541 0.884 0.923 0.509 0.956 0.971 
Coordination degree 0.399 0.329 0.264 0.247 0.274 0.343 0.343 0.279 0.431 0.364 
WRS Coupling degree 0.315 0.333 0.325 0.333 0.322 0.332 0.320 0.320 0.318 0.318 
Coordination degree 0.225 0.220 0.179 0.182 0.218 0.214 0.200 0.205 0.231 0.204 
Figure 2

Coupling degree and coordination degree of the water resource system and subsystems in the study area.

Figure 2

Coupling degree and coordination degree of the water resource system and subsystems in the study area.

Coupling degree and coordination degree of subsystems in the water resource system

Figure 2(a) shows the coupling degrees between the resource subsystem and the social, economic and ecological subsystems, which are mainly concentrated in the intervals [0.50–0.60], [0.50–0.80], and [0.80–1.00], respectively. This result indicates that the resource and social and economic subsystems are in a running-in stage, showing a strong degree of interaction. The resource subsystem and ecological subsystem are in a high coupling stage; the interaction between them is very strong.

Figure 2(b) shows the coordination degrees between the resource subsystem and each of the other subsystems, which are mainly concentrated in the interval [0.20–0.40]. This result indicates that the resource subsystem in the study area is in a barely coordinated stage with each other subsystem, and their coordinated development is at a lower level, which does not produce a good benefit. However, the evolution trends of the coordination degree between the resource subsystem and the social, economic and ecological subsystems are quite different, showing trends of fluctuating decrease, fluctuating rise, and decrease followed by rise, respectively. These varying trends indicate that the coordination between resources and social subsystems is not improved, but the coordination between resources and the economic and ecological subsystems shows a trend of improvement.

Coupling degree and coordination degree of the water resource system

Figure 2(c) and 2(d) show the coupling degree ([0.30–0.35]) and the coordination degree ([0.18–0.24]) of the water resource system, respectively. These values are derived from formula (9) based on the coupling coordination degree of each subsystem. The coupling degree of the water resource system is in an antagonistic stage, which indicates that the interaction between subsystems of the water resource system is low, and the system lacks cohesion. The annual average coordination degree of the water resource system is 0.208 (see Table 3), which shows that the system is in a barely coordinated stage, and the level of systematic coordination and orderly development of the water resource system is low. Especially in 2007 and 2008, when the coordination degrees reached 0.179 and 0.182, respectively, the system was in a maladjustment and recession stage, and the lowest levels of harmony and consistency of the system were reached.

DISCUSSION

Coupling degree and coordination degree of subsystems in the water resource system

The average annual growth rates of C7–C10 in the social subsystem during the study period were 0.07%, 0.92%, 3.37% and 2.46%, respectively, which demonstrates that the per capita domestic water consumption (C9) is the main index of the social subsystem. This finding indicates that the study area promotes an increase in per domestic capita water consumption in the process of urbanization, which to some extent leads to a sharp increase in the water resource exploitation rate (C1, growth rate is 8.33%) and the water consumption per unit land area (C2, growth rate is 33.61%). This may be the reason for the high coupling degree and the fluctuating decrease in the coordination degree between the resource and social subsystems. In view of this finding, in pursuit of urbanization, people should be encouraged to save water and promote the harmonious development of water resources and society.

The average annual growth rates of the indexes C11–C15 in the economic subsystem during the study period were 17.22%, 3.95%, 2.57%, −8.17% and 0.53%, respectively, which shows that the GDP per capita (C11) is the main indicator of the economic subsystem. The proportion of primary industry (C12) increased by 39.52%, while the water resource content per unit land area (C3) and the consumption degree of groundwater resources (C6) of the resource subsystem increased by 25% and 21.05%, respectively. This result indicates that the development of the regional agricultural economy may be the reason for the high coupling degree and the fluctuating rise in the coordination degree between the resource and economic subsystems. During the study period, the decreases in farmland water consumption intensity (C13) and industrial water consumption intensity (C14) in the study area reduced the consumption of surface water resources to a certain extent (C5, decreased by 3.85%). This finding indicates that in the study area, attention should be paid to the effective utilization rate of agricultural irrigation water in the process of economic development, and on this basis, accelerates the development of secondary and tertiary industries, which is conducive to the coordinated development of water resources and economy.

The average annual growth rates of C16–C19 in the ecological subsystem were 4.38%, 0.48% and −1.93%, respectively, which indicates that the environmental water use rate (C16) is the main indicator of the ecological subsystem. During the period 2005–2008, the environmental water use rate and the soil erosion rate (C19) in the study area increased by 30.44% and 2.46%, respectively, which resulted in a decrease in natural water resources to some extent (7.94%) in this area. This may be the main reason for the high coupling degree and the sharp decrease in coordination degree between the resource and ecological subsystems. Since 2009, with the increase in forest cover (C18, increased by 11.75%), the soil erosion in the study area has been alleviated (decreased by 21.28%), which improved the amount of natural water resources in the study area to some extent. This may be the main source of the increasing trend of resource and ecological subsystem coordination in 2009–2014. Thus, the study area should attach importance to the protection of the ecological environment, coordinate its resource capacity and ecological water consumption, and promote the coordinated development of water resources and the ecological environment.

Coupling degree and coordination degree of the water resource system

The annual coupling degree and coordination degree of the water resource system are 0.326 and 0.208, respectively, which shows that the coordination of the water resource system in the study area is poor. The overall coordination of the water resource system is derived from the coupling degree and coordination degree of the subsystems. There is high coupling and low coordination between the resource and social, economic and ecological subsystems, which indicates that the internal subsystem interaction with the water resource system has a high degree of influence, but they have poor coordination with each other. This difference seriously affects the coordinated development of the water resource system and leads to the low coupling and coordination degrees of the water resource system. Therefore, improving a harmonious development relationship among the subsystems is the key to promoting the coordinated development of the water resource system.

Advantages and disadvantages of the research methods

Compared with the static coupling coordination model (Li et al. 2012b), the dynamic coupling coordination model proposed in this paper fully considers the dynamic spiral relationship in the interaction process of each system. This model can be used to comprehensively study the dynamic, nonlinear and other complex characteristics of the evolution process of a water resource system. In addition, compared with a single dynamic coupling degree model (Ma et al. 2016), this model increases the dynamic coordination degree of the water resource system, which not only can describe the degree of mutual restriction among the elements of the system or system but can also reveal the benign interaction between them more fully and reflect the degree of harmony between the elements of the system or system in the process of development. Moreover, the method of standard deviation is used to avoid outliers after the raw data are standardized, and the disturbance of the parameters required in the evolution equations of the subsystems by the outliers is reduced.

In view of the water resource problems in the study area, such as the overexploitation of water resources and unequal distribution of water resources, this paper focuses on the harmonious relationship between water resources and the social, economic and ecological environment, so it does not consider the dynamic coupling and coordination between social, economic and ecological subsystems. In future work, we intend to study the coordinated development of the regional ecological environment and social economy from the perspective of the ecological environment.

CONCLUSIONS

Based on the compound characteristics of WRS, an evaluation index system of the coordinated development of WRS was established considering the four aspects of resources, society, economy and ecology. Individual standard deviation was introduced to improve traditional entropy to calculate the index weight. A dynamic coupling and coordination model was proposed to study the coordinated development of the resource and social, economic and ecological subsystems as well as the entire water resource system. The results show that the coordination of the water resource system in the study area is at a low level, the ability of coupling and coordination among subsystems is poor, and the subsystems show different varying trends of coordination. Therefore, improving the level of coupling and coordination among subsystems is the key to promote the coordinated and sustainable development of the water resource system. The dynamic coupling coordination degree model proposed in this paper can dynamically determine the variation of the coordinated development of a water resource system from the local level to the entire system. Based on the results of the analysis, the risk factors affecting the coordinated development of the water resource system can be obtained, which provides a reliable basis for the coordinated development of water resources and society, economy and ecology.

ACKNOWLEDGEMENTS

Many thanks to the National Natural Science Foundation of China (No. 51609039), the China Postdoctoral Science Foundation funded project (No. 2016M601410) and the Heilongjiang Postdoctoral Science Foundation funded project (No. LBH-Z16025).

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