Prediction of Chinese Automobile Growing Trend Considering Vehicle Adaptability based on Cui–Lawson Model

Since the famous Lotka–Volterra competition model [18] has simplified the intermediate competitive process [19], a Cui–Lawson model, shown in Equation (1), was proposed to describe the relationship between non-linear population growth and resource limitation which can be applied to more complex population behaviour analysis: (1)dXdt=μc*X1−X/Xm*1−X/Xm′{{dX} \over {dt}} = \mu _c^*X{{1 - X/X_m^*} \over {1 - X/{{X'}_m}}} where X is the population density at time t; Xm*X_m^* is the environmental capacity; μc*\mu _c^* is the maximum specific rate of population growth under certain environmental conditions and Xm′{X'_m} is a nutrient parameter related to environmental resource conditions and the population's affinity to resources.

There is a production–consumption–scrap life cycle in the automobile market, and there are inputs and outputs of vehicles. So, we consider that the competitive environment is a typical open system. Moreover, vehicles with different power sources have different energy demand. Therefore, we constructed a six-population competition model under open system condition with different nutritional requirements to reflect the adaptability of vehicle types with different power sources to certain environmental characteristics. The density growth rate of vehicle type i can be shown in the following equation: (2)dXidt=μci*Xi1−(Xi+∑j=1,j≠i6aijXj)/Xmi*1−(X1+∑j≠i,j=16aijXj)/Xmi′{{d{X_i}} \over {dt}} = \mu _{ci}^*{X_i}{{1 - ({X_i} + \sum\limits_{j = 1,j \ne i}^6 {a_{ij}}{X_j})/X_{mi}^*} \over {1 - ({X_1} + \sum\limits_{j \ne i,j = 1}^6 {a_{ij}}{X_j})/{{X'}_{mi}}}} where X_i is the density of vehicle type i, i = 1, 2, . . . , 6; μci*\mu _{ci}^* is the maximum specific rate of population growth under certain environmental conditions of vehicle type i, μci*=μci−Di\mu _{ci}^* = {\mu _{ci}} - {D_i} , D_i is population mortality rate. Xmi′=ki/ai+Xmi{X'_{mi}} = {k_i}/{a_i} + {X_{mi}} is the nutrient parameter of vehicle type i, X_mi is the environmental capacity of vehicle type i. Xmi*X_{mi}^* is the maximum density of vehicle type i, Xmi*=1−Di/μci1−(Di/μci)(Xmi/Xmi′)XmiX_{mi}^* = {{1 - {D_i}/{\mu _{ci}}} \over {1 - ({D_i}/{\mu _{ci}})({X_{mi}}/{{X'}_{mi}})}}{X_{mi}} . Obviously, Xmi*X_{mi}^* will be less than X_mi in general. a_ij is the competition coefficient of population j to population i, and it represents how much population j per unit quantity is equivalent to population i. The positive or negative value of a_ij represents the influence nature of population j on population i, and the absolute value represents the influence intensity.

In this article, six populations, namely traditional vehicle, pure electric vehicle, hybrid electric vehicle, gas–fuel vehicle, fuel cell vehicle and biofuel vehicle, will be targeted predict trend by population competition analysis. In the process of competing, vehicles of various energy source types will be produced and then scrapped. Therefore, the competitive system of various energy source vehicles is defined as an open system. At the same time, different types of vehicles use different energy sources, for example, the nutritional requirements of competing species in the system are not the same. Based on the earlier analysis, the interspecific competition equations (3)–(8) were constructed under open system condition with different nutritional requirements for competing species. (3)dX1dt=μc1*X11−(X1+∑j=26a1jXj)/Xm1*1−(X1+∑j=26a1jXj)/Xm1′{{d{X_1}} \over {dt}} = \mu _{c1}^*{X_1}{{1 - ({X_1} + \sum\limits_{j = 2}^6 {a_{1j}}{X_j})/X_{m1}^*} \over {1 - ({X_1} + \sum\limits_{j = 2}^6 {a_{1j}}{X_j})/{{X'}_{m1}}}}(4)dX2dt=μc2*X21−(X2+∑j=1,j≠26a2jXj)/Xm2*1−(X1+∑j=1,j≠26a2jXj)/Xm2′{{d{X_2}} \over {dt}} = \mu _{c2}^*{X_2}{{1 - ({X_2} + \sum\limits_{j = 1,j \ne 2}^6 {a_{2j}}{X_j})/X_{m2}^*} \over {1 - ({X_1} + \sum\limits_{j = 1,j \ne 2}^6 {a_{2j}}{X_j})/{{X'}_{m2}}}}(5)dX3dt=μc3*X31−(X3+∑j=1,j≠36a3jXj)/Xm3*1−(X1+∑j=1,j≠36a3jXj)/Xm3′{{d{X_3}} \over {dt}} = \mu _{c3}^*{X_3}{{1 - ({X_3} + \sum\limits_{j = 1,j \ne 3}^6 {a_{3j}}{X_j})/X_{m3}^*} \over {1 - ({X_1} + \sum\limits_{j = 1,j \ne 3}^6 {a_{3j}}{X_j})/{{X'}_{m3}}}}(6)dX4dt=μc4*X41−(X4+∑j=1,j≠46a4jXj)/Xm4*1−(X4+∑j=1,j≠46a4jXj)/Xm4′{{d{X_4}} \over {dt}} = \mu _{c4}^*{X_4}{{1 - ({X_4} + \sum\limits_{j = 1,j \ne 4}^6 {a_{4j}}{X_j})/X_{m4}^*} \over {1 - ({X_4} + \sum\limits_{j = 1,j \ne 4}^6 {a_{4j}}{X_j})/{{X'}_{m4}}}}(7)dX5dt=μc5*X51−(X5+∑j=1,j≠56a5jXj)/Xm5*1−(X5+∑j=1,j≠56a5jXj)/Xm5′{{d{X_5}} \over {dt}} = \mu _{c5}^*{X_5}{{1 - ({X_5} + \sum\limits_{j = 1,j \ne 5}^6 {a_{5j}}{X_j})/X_{m5}^*} \over {1 - ({X_5} + \sum\limits_{j = 1,j \ne 5}^6 {a_{5j}}{X_j})/{{X'}_{m5}}}}(8)dX6dt=μc6*X61−(X6+∑j=15a6jXj)/Xm6*1−(X6+∑j=15a6jXj)/Xm6′{{d{X_6}} \over {dt}} = \mu _{c6}^*{X_6}{{1 - ({X_6} + \sum\limits_{j = 1}^5 {a_{6j}}{X_j})/X_{m6}^*} \over {1 - ({X_6} + \sum\limits_{j = 1}^5 {a_{6j}}{X_j})/{{X'}_{m6}}}}

Equations (3)–(8) constitute the prediction model for the development trend of environmental adaptability of six energy source kinds of vehicles under open condition. In the following section, we will explain the parameter selection of simulation prediction in detail.

According to the geographical location, economic development and climatic conditions, China can be divided into six regions, namely north China, northeast China, east China, south China, southwest China and northwest China. The socio-economic status and geographical characteristics of the six major regions in China are shown in Table 2.

As shown in Table 2, in terms of vehicle ownership, the total number of civil motor vehicles in east China is the highest. The terrain of east China is dominated by hills, basins and plains. East China generates 38% of GDP with 9% of the land area. The second region is south China, with a total of 58.35 million civilian motor vehicles, in which population and GDP account for 28.4% and 26.9%, respectively. In order of vehicle ownership, north China, southwest China, northeast China and northwest China are followed. In terms of the number of motor vehicles per 100 people, north China is the highest with 20, followed by eastern China with 19, northeast and northwest China with 16 and south and southwest China with 15 and 13 motor vehicles, respectively.

According to the traffic administration bureau of the ministry of public security published data from 2015 to 2019, pure electric vehicles account for about 80% of new energy vehicles, and currently all motor vehicles account for a maximum of 1.3%. We assume that the proportions of various types of vehicles in different regions are the same to better analyse the adaptability of vehicles with different power sources to regional environmental conditions. Population density and economic development level are important factors influencing the growth rate of motor vehicles, while geographical characteristics and climatic conditions highly influence the choice of vehicle types. According to the development trend of motor vehicle ownership, regional economic development and climatic and geographical conditions in recent years, relevant parameters of each region were set.

Consider north China as an example: this region has a high level of economic development and the highest per capita motor vehicle ownership. The terrain is dominated by plains. There is no extreme cold in the climate. The adaptability of all kinds of power vehicles is good. Thus, the parameters that will be used are given in Table 3.

To investigate the performance of population competition, we execute a variety of case studies with different presetting parameters. All the simulations are performed on a personal computer with 1.80 GHz CPU and 4.00 GB memory, and the algorithms are coded in Matlab R2018b. The prediction result of north China can be seen in Figure 1(a). Similarly, simulation parameters are set in the other five regions according to the regional characteristics, and the results are shown in Figure 1(b)–(f).

Fig. 1

As shown in Figure 1(a), the traditional vehicle ownership presents a parabolic development trend that will increase steadily in 10 years. It is estimated that the traditional car ownership will reach the peak value around 2030, about 40 million, and then decrease. Among the new energy vehicles, the ownership of pure electric vehicle also presents a parabolic development trend, with a low speed growth in the past 10 years. Then, encouraged by the government's promotion and technological progress, the ownership of pure electric vehicles will grow rapidly in the next 10–30 years. Thirty years later, as technology improved significantly, the ownership of zero-emission fuel cell vehicle will increase rapidly, showing a S-shape, and eventually become a mainstream power source. The development trend of hybrid electric vehicle is similar to the parabolic shape of pure electric vehicles ownership. But earlier, the hybrid vehicle has no advantage in technology maturity and the government subsidies compared with pure electric vehicles. Moreover, in terms of environmental protection, hybrid vehicle cannot be compared with hydrogen fuel cell vehicle. However, the traditional vehicle will drop into a period of decline, when the hybrid vehicle can obtain a relatively loose development and environment. Due to the limitation of living environment and development, the ownership of gas–fuel cell vehicle and biofuel vehicle has been at a low level of development.

As detailed in Figure 1(b), the development trend of traditional vehicle in northwest China also presents a parabolic sharp, with the highest ownership gained after 17 years. But unlike in north China, traditional vehicle will be the most kind for the next 40 years. This indicates that the influence of climate and terrain condition in northeast China on the adaptability of vehicles with various power sources is mainly reflected in the proportion of low temperature weather throughout the year which is much higher than that in north China. At this time, the endurance of pure electric vehicles is greatly affected.

Comparing Figure 1(c) and (d) shows that similar behaviour was observed in both east China and south China, with a major development of pure electric vehicle at first stage and fuel cell vehicle at a later stage, although the vehicle ownership in east China is higher.

As illustrated in Figure 1(e), the development trend is in line with the trend previously shown in east China. However, in the long term, the development trend of fuel cell vehicles in southwest China is better than that of hybrid electric vehicles.

As indicated in Figure 1(f), the development trend of northwest China is noticeably different from trends in the other five regions. It is obvious that the hybrid electric vehicle increases rapidly from 2030 to 2040. To the knowledge of the authors, the possible reasons may be as follows. First, high altitude and cold weather have great influence on the power performance of fuel cell vehicle and the endurance of pure electric vehicle, respectively. Thus, the adaptability of these two energy source vehicles that have a good development in other regions in northwest China is much lower than hybrid electric vehicle. Besides, the development stage lags in other regions due to their backward economy.

In general, based on the accumulated industry advantages of policy bias, pure electric vehicles have certain advantages in cost and infrastructure construction and will continue to develop rapidly soon. However, in the later stage, with the promotion of energy transformation and the continuous development of technology, cost and infrastructure, fuel cell vehicles have greater development space. The social and economic differences between regions are the main reason why the competitive market of automobiles is in different stages. In addition, low temperature, high altitude and other special conditions will limit the development space of some vehicles in the region.