The article explores the evolution of regional spatial differences and has important practical significance for promoting the coordinated development of regional tourism. The article analyzes the characteristics of the spatial evolution of the economic tourism pattern from 2010 to 2020. The study found that the development of the regional tourism economy is on the rise, and the development is not balanced. The spatial self-organization of economic development is getting stronger and stronger, and the spatial economic distribution is different. Then this article analyzes the main factors that cause this spatial distribution and proposes corresponding solutions. This provides a theoretical basis for reducing the gap in the tourism economy between regions and promoting the coordinated development of the regional tourism economy.

#### Keywords

- Economic pattern
- Spatial evolution
- Spatial variability function
- Regional tourism economy

#### MSC 2010

- 62H20

The spatial evolution of the economic pattern is the result of regional interaction, and it is also the external manifestation of the continuous transformation of economic relations in the regional space and the internal structure. Since the reform and opening up, the spatial differences in China's regional economic structure have increased significantly. Chinese and foreign scholars have always maintained a strong research interest in it. “Growth pole, core-periphery, gradient transition, polarization-diffusion, point-axis,” etc., have become the theoretical sources of the spatial evolution of the economic structure. The current academic circles are using increasingly mature methods and mean to study the temporal and spatial evolution of the national, provincial, and economic patterns.

The “C-type” economic zone around the Bohai Sea includes the Liaodong Peninsula, Beijing-Tianjin-Hebei, and the Shandong Peninsula. It is the “engine” for the development of northern China, and it is also the core area distributed among urban agglomerations, industrial clusters, and port clusters. The GDP in 2020 will account for 25.32% of the country's total. The “C-type” economic zone in the Bohai Sea Rim has significant economic differences, major imbalances, and serious vicious competition [1]. Its resources and technological advantages cannot be effectively transformed into economic advantages. Its level of economic integration is much lower than the Yangtze River Delta and the Pearl River Delta. There are few achievements in the evolution of the economic structure of the “C-type” economic zone around the Bohai Sea. Based on this, we take the Bohai Rim “C-type” economic zone as an example and use per capita GDP as a measurement indicator to conduct research. At the same time, we use the three-time sections in 2000, 2010, and 2020 as the basis and use ESDA related analysis to discuss the economy [2]. The spatial evolution characteristics of the pattern. At the same time, we describe the evolutionary law and overall trend of the economic structure. This article aims to provide theoretical support for governments at all levels to formulate regional development policies.

The article introduces GlobalMoran'sI, Getis-OrdGeneralG, and

(1) GlobalMoran'sI
_{ij}_{i}_{j}^{2} is the sample variance. We use the Z value method to test:

(2) Getis-OrdGeneralG
_{ij}_{i}_{j}

(3)

_{t1}, _{t2} is the per capita in year _{1}, _{2}, and

The spatial variogram is a unique basic means to describe the randomness and structure of regionalized variables. It can well express the spatial heterogeneity and correlation of geographic variables.

_{i}_{i} + h_{i}_{i}_{0} (nugget value) at _{0} (base station value), the maximum spatial correlation distance is _{0}, the greater the range of change. The trend toward 0 is a continuous change, and the nugget coefficient _{0} / (_{0}) reflects the degree of change. The fractal dimension ^{(4−2D)}.

We take Shandong Province, Liaoning Province, Hebei Province, Beijing, and Tianjin in the “C-type” economic zones around the Bohai Sea (referred to as “C-type” economic zones, Shandong, Liaoning, Hebei, Beijing, and Tianjin, respectively) as the research objects. At the same time, the article uses 318 counties as the research unit and revises the administrative divisions following the principle of comparability [6]. The per capita GDP data are all sourced from the “China City Statistical Yearbook.”

We use formulas (1) and (2) to calculate GlobalMoran'sI and GeneralG in 2000, 2010, and 2020 using GeoDA software. Table 1 shows that Moran'sI estimates for the three years are all greater than zero. It passed the significance test, and the effect was significant. This shows that since 2000, the “C-type” economic zone has had a high degree of spatial aggregation in areas with similar economic development levels. The degree of aggregation has continued to increase over time [7]. The G(d) of the three years are all greater than 0 and higher than E(d). This shows that economic development is concentrated in several hot spots. Among them, G(d) was the lowest in 2000. This shows that the phenomenon of high-value agglomeration is not obvious. In 2020, the difference between G(d) and E(d) was the largest. This shows that the spatial agglomeration trend of economic development is constantly increasing.

Moran'sI and GeneralG of GDP per capita in “C-type” economic zones

Moran'sI | ||||||
---|---|---|---|---|---|---|

0.1882 | 5.4233 | 0.0173 | 0.0165 | 2.4304 | ||

0.3306 | 10.1467 | 0.0183 | 0.0165 | 3.2766 | ||

0.4661 | 13.6857 | 0.0189 | 0.0165 | 4.799 |

We use formula (3) to calculate

First, there are obvious differences in the overall spatial pattern of economic hotspots. In the three years, the Beijing-Tianjin-Tangshan metropolitan area, the Shenyang-Dalian economic belt, and the Shandong Peninsula urban agglomeration all showed the characteristics of hotspot structure. Big cities such as Beijing, Tianjin, Shenyang, Tangshan, Dalian, Dongying, Yantai, Weihai, Jinan, Qingdao, and their surrounding areas have become the most dynamic hotspots or sub-hotspots [8]. The development of the tourism economy tends to be coastal. Some counties and cities in western Liaoning, northern Hebei, southern Hebei, inland counties and cities in western Shandong, and the inter-provincial adjacent areas of Shandong-Hebei and Liao-Hebei, are always low-value clusters of cold spots or sub-cold spots.

The second is a certain change in the number of different types of districts. The proportion of hot spots will drop from 11% in 2000 to 8% in 2020. Factors of production gather in coastal areas. Wafangdian City, Dongying City District, Wudi County, Penglai City, Longkou City, Zhaoyuan City, Qingdao City District, Rizhao City District Panshan County, Tangshan City District, and Zhangqiu City in the inland area have become hot spots. Its economy is developing rapidly. The number of cold spots decreases first and then increases. The proportions in 2000, 2010 and 2020 are 44.97%, 29.87% and 45.60% respectively. The most obvious changes are in the adjacent areas of Shandong and Hebei.

Third, most of the hot spots that have not changed are concentrated in coastal areas. The districts include Yantai City, Weihai City, Wendeng City, Rongcheng City, Dalian City District, etc. The cold spot areas that have not changed are concentrated in traditional farming areas. The regions include Fuxin Mongolian Autonomous County, Jianping County, Lingyuan City in Western Liaoning, Heze City in Southwestern Shandong, Zhangjiakou City in Northern Hebei, and Julu County in Southern Hebei and the surrounding areas. The economic development of these places is gradually slow, and they are at a disadvantage in the fierce market economy competition (Figure 1).

We use formulas (3) and (4) and ArcGIS 10.0 software to analyze the evolution characteristics of economic growth hot spots from 2000 to 2010 and 2010 to 2020. Overall, the Moran'sI estimates for the two periods are 0.3323 and 0.3615, respectively, passing the significance test. This shows that the economic growth of the “C-type” economic zone has strong spatial agglomeration and stability characteristics, the agglomeration pattern is gradually increasing, and the spatial autocorrelation is relatively obvious. This is consistent with the spatial agglomeration characteristics of economic development in 2000, 2010, and 2020. 1) The spatial transition characteristics of the economic growth hotspot area are obvious and large. During the two periods, the number of hot spots dropped from 55 to 21, and no administrative unit remained in the hot spot. This shows that the high economic growth rate of the “C-type” economic zone is transforming quickly between different counties, and the cold spot area also shows strong evolution characteristics. The number has increased from 47 to 97. 2) From the evolution process of hotspots and coldspots in various periods, the hotspots were relatively scattered and irregular and distributed in the form of clumps from 2000 to 2010. Regions include Tangshan Group (i.e., Tangshan City District, Qian’an City, Lulong County, Luan County, Luli County, Letting County, and Luannan County), Jidongnan Group (i.e., Cangzhou City District, Huanghua City, Cang County, Qing County, Dacheng County, Hejian County, Suning County, Xian County, Renqiu City, Botou City, Gaoyang County, etc.), Southwest Hebei Group (i.e., Shijiazhuang City District, Luquan City, Jingxing County, Yuanshi County, Zanhuang County, Luancheng County, Zhengding County, Xinji City, etc.), the Yellow River Delta Group (i.e., Dongying City District, Kenli County, Lijin County, Zhanhua County, Boxing County, Binzhou City District, and Huimin County), Jining Group (Namely Zoucheng City, Yanzhou City, Qufu City, and Sishui County), Weihai City and Zhangqiu City. The sub-hot spots accounted for the highest proportion (48.15%). It is distributed in most counties and cities in southern Shandong, eastern Shandong, central Shandong, southern Hebei, and eastern Liaoning. The cold spots are concentrated west of Liaoning, northern Hebei, and Heze city in southwestern Shandong. From 2010 to 2020, the hotspots migrated inland in northwestern Liaoning and were distributed in a zonal pattern. The above shows that the economic disparity within the provinces of the “C-type” economic zone is shrinking, and the inter-provincial economic disparity is gradually increasing. It is prominently reflected in the spatial change trajectory of the hot spot area and the cold spot area (Figure 2).

Use formula (5) to assign per capita GDP as a spatial variable to the geometric center point of each county unit. Define the sampling step length of 300km to calculate the variogram. Fit the sample data and select the model with the best effect and best fit. We calculate the fractal dimension in each direction and perform Kriging interpolation to obtain the fitting parameters (Table 2), the fractal dimension (Table 3), and the evolution map (Figure 3).

Fitting parameters of the various function of the economic structure of the “C-type” economic zone

Related process | Nugget value | Abutment value | Nugget coefficient | Fitting the model | Decisive factor | |
---|---|---|---|---|---|---|

159300 | 0.1275 | 0.308 | 0.414 | Exponential | 0.992 | |

135700 | 0.0724 | 0.3408 | 0.2124 | Exponential | 0.992 | |

117700 | 0.083 | 0.393 | 0.2112 | Exponential | 0.96 |

The fractal dimension of the variability function of the economic structure of the “C-type” economic zone

years | 2000 | 2010 | 2020 | |
---|---|---|---|---|

D | 1.873 | 1.799 | 1.081 | |

R2 | 0.994 | 0.992 | 0.965 | |

D | 1.85 | 1.751 | 1.762 | |

R2 | 0.985 | 0.985 | 0.988 | |

D | 1.845 | 1.768 | 1.757 | |

R2 | 0.954 | 0.994 | 0.972 | |

D | 1.895 | 1.833 | 1.893 | |

R2 | 0.898 | 0.946 | 0.877 | |

D | 1.905 | 1.841 | 1.792 | |

R2 | 0.86 | 0.953 | 0.908 |

The correlation degree drops significantly at a given step size. The data decreased from 159,300 in 2000 to 117,700 in 2020 (Table 2). This shows that the radiation range of the spatial correlation effect of the economic development of the “C-type” economic zone has been continuously reduced, and the radiation trickle effect of big cities has begun to weaken. The abutment value continues to increase, the nugget value first decreases and then increases, and the nugget coefficient gradually decreases. This shows that the economic development space of the “C-type” economic zone is affected by both structural factors and random factors. Under the situation of increasing economic, spatial differences, the influence of structural differentiation caused by spatial autocorrelation is more significant [9]. The spatial variation fitting model selected by the least square method is an exponential model. The coefficients of determination are all above 90%. The good fitting effect and high degree indicate that the spatial self-organization of the economic development pattern of the “C-type” economic zone is becoming stronger and stronger.

The omnidirectional fractal dimension is reduced from 1.873 in 2000 to 1.081 in 2020, far from the ideal value of homogeneous distribution 2. The fitting coefficient of determination is high but gradually decreases. The data dropped from 0.994 in 2000 to 0.965 in 2020 (Table 3). This shows that the uniformity of economic development in all directions of the “C-type” economic zone is continuously decreasing. The structural differentiation caused by spatial autocorrelation is becoming more obvious, and the economic difference gradually increases. Among the other four directions, only the east-west fractal dimension is relatively high and stable. The values for the three years are 1.895, 1.833, and 1.893. This shows that economic development has better homogeneity and smaller spatial differences. The fractal dimensions of the south-north direction, northeast-southwest direction, and southeast-northwest direction decreased significantly. This shows that the spatial gap in economic development is gradually widening.

There is a certain regularity and continuity in the evolution of the economic structure of the “C-type” economic zone, and the morphological distribution has internal connections and structural characteristics (Figure 3). The spatial differences in economic development have obvious hierarchical characteristics. The economy is centered on the eastern coast and slopes towards the surrounding areas. Over time, the level of economic development has generally increased. The southwest and northwest inland are always at a “trough.” The peaks in 2000 were concentrated in coastal cities or resource-based cities, while northern Hebei, southern Hebei, and southwestern Shandong lag. In 2010, the Shandong Peninsula urban agglomeration quickly developed into a peak and high point agglomeration area. Several “columnar peaks” appeared in Luxi and Lunan, drove by its radiation [10]. Driven by the two major cities of Beijing and Tianjin, Jixi and Northwest Hebei have also developed but are still relatively backward. The peaks in 2020 are concentrated in coastal areas and inland metropolitan areas, followed by the surrounding areas of major cities such as Beijing, Jinan, Qingdao, Shenyang, and Dalian. Mountain and hilly areas, traditional farming areas, and Bashang plateau areas (including western Hebei, southern Hebei, and southwestern Shandong) are the lowest level.

Since the opening of coastal cities in the “C-type” economic zone in 1984, coastal areas have achieved rapid development using preferential policies. Subsequently, a series of coordinated development policies aimed at various provinces or nearby provinces have been issued. The content includes Shandong Peninsula city group, revitalization of old industrial bases, Beijing-Tianjin-Hebei Metropolitan Area, Tianjin Binhai New Area, Shenyang Economic Zone, Liaoning Coastal Economic Zone, Yellow River Delta High-Efficiency Ecological Economic Zone, Capital Economic Circle, Shandong Peninsula Blue Economic Zone, etc. The economic gap within the province has narrowed. Still, there is no strategic deployment and planning for the entire “C-type” economic zone and a lack of a unified coordination mechanism. Since 2014, the implementation of the “Breakthrough in Northwest Liaoning” strategy, the pilot transformation of the resource-based city of Fuxin, the construction of the Tieling ecological new city, the radiant drive of the Shenyang-Dalian Economic Belt, and the linkage with the eastern Inner Mongolia region, etc. This makes Northwest Liaoning a hot spot for economic growth from 2010 to 2020. Inland Hebei and Heze City in southwestern Shandong have been at the bottom of the policy and lacked the vitality and engine for economic development.

The long-term unbalanced economic industrial base has not changed significantly, and the economic core has not yet been formed. Liaodong Peninsula, Beijing-Tianjin-Hebei, and Shandong Peninsula form their systems, with Dalian, Beijing, Tianjin, and Qingdao becoming their respective leaders. Beijing relies on administrative and cultural resources to establish a superior position, and Tianjin has introduced many funds, policies, business concepts, and advanced technology [11]. High-tech, sophisticated, and cutting-edge industries dominate the two cities. Shandong Province is constantly seeking industrial upgrades in a mix of industry and agriculture and pays more attention to an export-oriented economy. Liaoning Province focuses on the development of heavy industries such as equipment manufacturing and raw material processing. Hebei Province is dominated by traditional agriculture and has the weakest economic strength. At present, in addition to almost all traditional industries such as chemical industry, coal, and electric power, all provinces and cities are competing to develop high-tech industries such as biopharmaceuticals, new materials, and electronic information. Structural convergence restricts the realization of the best association and maximum benefit of regional industries. The unclear positioning of port functions has also delayed the pace of economic integration, and the trend of widening economic differences is unavoidable in the short term.

Coastal cities in the “C” economic zone rely on a complete port transportation system and their spatial location advantages with developed countries such as South Korea and Japan. Vigorously develop an open economy with a relatively large peak height. The small and medium-sized counties and cities in the inter-provincial neighboring Hebei and Southwest Shandong and Shandong and Liaoning are located inland. Poor transportation location and high factor flow cost are severe constraints on the economic development of the region. This leads to a relatively weak overall level. Since 2000, the evolution of hotspots has revolved around the Shenyang-Dalian Line, Beijing-Tianjin Line, and Jinan-Qingdao Line to form three major hotspot clusters: Shenyang-Dalian Economic Belt, Beijing-Tianjin-Tangshan Metropolitan Area, and Shandong Peninsula City Cluster. In particular, the opening and operation of highways, high-speed railways, and air transportation lines have driven the rapid economic development of major transportation nodes along the lines and their neighboring cities.

Using the spatial variogram to study, it is found that there is a certain regularity and continuity in the evolution of the economic structure of the “C-type” economic zone. Space self-organization is enhanced. The study found that the spatial autocorrelation of economic development is significant. The hot spots are concentrated in the Beijing-Tianjin-Tangshan metropolitan area, the Shenyang-Dalian Economic Belt, and the Shandong Peninsula urban agglomeration. Regions include coastal counties, metropolitan, municipal districts, and surrounding counties. Other inland and inter-provincial fringes are cold spots. The economic growth hotspot area has made a significant leap. Relatively scattered and irregular mass distribution from 2000 to 2010. From 2010 to 2020, it was distributed in the northwestern region of Liaoning in a stripe pattern, and the economic gap within the province narrowed, and the inter-provincial economic gap increased.

#### Fitting parameters of the various function of the economic structure of the “C-type” economic zone

Related process | Nugget value | Abutment value | Nugget coefficient | Fitting the model | Decisive factor | |
---|---|---|---|---|---|---|

159300 | 0.1275 | 0.308 | 0.414 | Exponential | 0.992 | |

135700 | 0.0724 | 0.3408 | 0.2124 | Exponential | 0.992 | |

117700 | 0.083 | 0.393 | 0.2112 | Exponential | 0.96 |

#### Moran'sI and GeneralG of GDP per capita in “C-type” economic zones

Moran'sI | ||||||
---|---|---|---|---|---|---|

0.1882 | 5.4233 | 0.0173 | 0.0165 | 2.4304 | ||

0.3306 | 10.1467 | 0.0183 | 0.0165 | 3.2766 | ||

0.4661 | 13.6857 | 0.0189 | 0.0165 | 4.799 |

#### The fractal dimension of the variability function of the economic structure of the “C-type” economic zone

years | 2000 | 2010 | 2020 | |
---|---|---|---|---|

D | 1.873 | 1.799 | 1.081 | |

R2 | 0.994 | 0.992 | 0.965 | |

D | 1.85 | 1.751 | 1.762 | |

R2 | 0.985 | 0.985 | 0.988 | |

D | 1.845 | 1.768 | 1.757 | |

R2 | 0.954 | 0.994 | 0.972 | |

D | 1.895 | 1.833 | 1.893 | |

R2 | 0.898 | 0.946 | 0.877 | |

D | 1.905 | 1.841 | 1.792 | |

R2 | 0.86 | 0.953 | 0.908 |

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mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Financial Crisis Early Warning Model of Listed 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