Nonlinear Dynamic Analysis of Urban Roads and Daytime Population

Transcription

1 Urban and Regional Planning 07; (): -6 doi: 0.648/j.urp Nonlinear Dynaic Analysis of Urban Roads and Daytie Population Shiqing Yan College of Urban and Planning, Yancheng Teachers University, Yancheng, China Eail address: To cite this article: Shiqing Yan. Nonlinear Dynaic Analysis of Urban Roads and Daytie Population. Urban and Regional Planning. Vol., No., 07, pp. -6. doi: 0.648/j.urp Received: February, 07; Accepted: February, 07; Published: March 9, 07 Abstract: Since the road syste can not eet the traffic deand generated by the daytie population, traffic congestion has restricted urban econoic and social developent. Based on nonlinear dynaics theory, this paper analyzes the relationship between the area of urban road and the daytie population. The result shows the nuber of urban daytie population is proportional to the area of urban road at steady state. The author also found that the increase of urban road area is constrained by the axiu road area of a particular area at the city. When the road area is fixed, the nuber of urban daytie population is inversely proportional to the travel intensity. Keywords: Urban Road, Urban Daytie Population, Nonlinear Dynaics. Introduction The daytie population refers to the people who are active in a particular area during the day, including people who are working, studying, shopping, travelling, visiting relatives and seeking edical treatent etc., and it also includes residential population who are not engage in econoic activities. There is a one-day cycle of population igrates between the city center and the outskirts of the city. During the day, a large nuber of people fro the city periphery to the central area of the city to engage in work, study, edical treatent, shopping, touris and other activities, which draatically increase the nuber of population in the city center. At night, the population flows in the opposite direction. The traffic deand arising fro the population igration and the daytie population engaged in other activities, which is the ain body of urban transport deand []. In the urban center area, the large density of daytie population and highly gathered people and traffic flow, this leads to traffic congestion []. Due to the sall population density and inadequate traffic deand, it is difficult to develop public transportation and it is inconvenient to travel for residents []. Many scholars have explored the relationship between urban transport and urban population, and achieved a lot of research results [4-8]. However, they usually analyze the ipact of urban population on urban transport in a general anner, and they ignore the effects of different coponents of urban daytie population on urban traffic. Nonlinear dynaics theory can quantify the relationship between objects and evolutionary echanis, and it is widely used to geographical sciences [9], environental science [0], atospheric sciences [] and anageent science []. On the basis of a deep understanding of the intrinsic dynaics and the evolutionary echanis of the objects, ipleent scientific and effective anageent, and then to predict, control and optiize the evolution process of the syste. In this paper, the author proposes nonlinear theory to investigate the dynaical relationship between the urban road area and the daytie population, and predict the developent tendency of the syste which consisted of daytie population and urban road. It has iportant theoretical and practical significance for urban planning and urban anageent.. Nonlinear Dynaics Model of Daytie Population and Urban Road Area According to the relationship between daytie population and urban road area, this paper proposed the following nonlinear dynaics odel:

2 Shiqing Yan: Nonlinear Dynaic Analysis of Urban Roads and Daytie Population dx = rx( ay x) dt dy x = Ry[ ( Ak + Bk + Ck) ] dt y where x is the total nuber of daytie population in a city or an area, y is the total area of road in that city or area. r and R are the growth rate of daytie population and road area, respectively. a is the nuber of population that can be accoodated by the unit road area at noral condition, ay is the axiu nuber of population that can be accoodated by all of the roads in a city. ay x is the reaining capacity of population that can be accoodated by the urban road. The nuber in the second equation of () is the restriction of regional resources, society and econoy on urban road - urban daytie population syste. The different coponents of a city's daytie population have different ipacts on the urban econoy and their transport deands are not the sae. k is the proportion of eployed population that counicating into the city in urban daytie population. A is the travel intensity of eployed population that counicating into the city, and the travel intensity is effected by the nuber of trips, travel distance, travel tie, and road area occupied by the trip. k is the proportion of non-eployed population that counicating into the city, including the population who coute into the city to go shopping, travel, edical treatent, visiting relatives and so on. B is the travel intensity of non-eployed population that counicating into the city. k is the proportion of the residential population, C is the travel intensity of the residential population. y is the axiu road area deterined by the regional resources, econoic and social conditions. ( Ak + Bk + Ck) x is the total traffic deand of x urban daytie population. ( Ak + Bk + Ck) is the y reaining capacity of urban road. Model () objectively reflects the constraint relations between the urban road area and the nuber of daytie population.. The Solution and Discussion of Equilibriu State.. The Solution of Equilibriu State dx dy Let = = 0, we can get the equilibriu state solutions dt dt of odel () are M (0,0) and y y N[ x0 =, y0 = ] Ak + Bk + Ck a( Ak + Bk + Ck).... Equilibriu State M (0, 0) According to the stability theory [], it is observed that () M (0,0) is an unstable saddle point, this iplies that the syste of urban road and urban daytie population will develop in saddle shaped and leave point M (0, 0).... Equilibriu State y y N[ x0 =, y0 = ] Ak + Bk + Ck a( Ak + Bk + Ck ) y Since T = a + a = r < 0, thus the Ak + Bk + Ck equilibriu state N is stable. According to the stability theory, when ry 4 R( Ak + Bk + Ck) > 0, the equilibriu state N is a stable node, and its dynaic behavior is a non-periodic curve or linear otion, when ry 4 R( Ak + Bk + Ck ) < 0, the equilibriu state N is a stable focus, and its dynaic behavior is quasi-periodic otion with varying aplitude. Based on the above analysis, we derive the following conclusions: () When r > 4 R( Ak + Bk + Ck)/ y, that is the growth rate of daytie population is larger than four ties of R( Ak + Bk + Ck)/ y, the syste of urban road and daytie population transfer to equilibriu state N with the tendency of non-periodic curve or linear otion and the final equilibriu state is stable. Because the oveent speed of node is very fast, thus that is not benefit to the stability of the syste. In reality, the growth speed of urban daytie population is too fast, and leads to a large nuber of econoic and social probles. () When r < 4 R( Ak + Bk + Ck)/ y, that is the growth rate of daytie population is saller than four ties of R( Ak + Bk + Ck)/ y, the syste evolves to equilibriu state N in the way of quasi-periodic otion with varying aplitude, and the equilibriu state is stable. The quasi-periodic otion with varying aplitude iplies the evolution of the syste of urban road and daytie population is stable. In fact, the oderate increase of daytie population in the urban core area is the perforance of econoic developent, industrial structure optiization and CBD functions increase. Therefore, it is eaningful to study the equilibriu state... Discussion of Equilibriu State Equilibriu state N has iportant practical significance, and we will further discuss it. Equilibriu state N shows () The nuber of urban daytie population x is proportional to the axiu road area that a city can afford y, and inversely to the unit travel volue of daytie population Ak + Bk + Ck. () The total area of urban roads y is proportional to the axiu road area that a city can afford y, and inversely to the road through capacity a( Ak + Bk + Ck), where a is the nuber of population that can be accoodated by the unit road area. () The nuber of daytie population is a ties of road area at steady state. We discuss it in detail in the following.

3 Urban and Regional Planning 07; (): Fix the Road Area, the Relationship Between the Nuber of Daytie Population x and the Travel Volue Ak + Bk + Ck In the unit travel volue of daytie population Ak + Bk + Ck, with the city CBD function, the nuber of eployed population and non-eployed population who go shopping, touris and consulting into the city center are definitely increase, that eans k and k are increase. Besides, with the iproveent of quality of life, shopping and physical activity of residents will increase, and then the travel density of residential population is difficult to decrease. Therefore, in order to reduce the travel volue of unite daytie population, we need to take different strategies for different daytie population, and discuss their ipacts on the nuber of daytie population x respectively. () Fix the road area, the relationship between the nuber of daytie population x and the travel intensity of eployed population A When the road area is fixed, the increase of travel intensity of eployed population that counicating into the city, which definitely leads to the increase of traffic deand, and then decrease the capacity of daytie population. We set y, k and Bk + Ck as constants, and nuerical siulation result as shown in figure. population as a result of changes in A, and the value ranges of A is fro % to 00%. With the increase of A, x gradually becoes saller. Thus decrease the travel intensity of eployed population who couting into city which could increase the capacity of urban daytie population. () Fix the road area, the relationship between the nuber of daytie population x and the proportion of residential population k In the urban daytie population, the larger the nuber of residential population who living in urban, the greater the urban space occupied by their residence and passage, and then reduce the capacity of urban daytie population. Here, we set y, Ak + Bk and C as constants, and the nuerical siulation result as show in figure. Figure. The relationship between the nuber of daytie population in cities and the proportion of the city-center residential population. Where the solid line ( x ), dot line ( x ), dash line ( x ) and dash dot line ( x 4 ) are corresponding to four conditions of Figure. The relationship between the nuber of daytie population x and the travel intensity of eployed population A. Where the solid line ( x ), dot line ( x ), dash line ( x ) and dash dot line ( x 4) are corresponding to four conditions of y taking the nuber of 0., 0., 0.5 and 0.7, respectively. k taking the nuber of 0.5, Bk + Ck taking the nuber of 0.4. Figure shows when y, k and Bk + Ck are constant, the relationship between the nuber of daytie population x and the travel intensity of eployed population A. Abscissa is the travel intensity of eployed population A and A > 0, the ordinate indicates the changes of the urban daytie Ak Bk + taking the nuber of 0.5, 0.6, 0.7, 0.8, and both C and y taking the nuber of.0. Figure shows when y, C and Ak + Bk are constant, the relationship between the nuber of daytie population x and the proportion of residential population k. Abscissa is the proportion of residential population and k > 0, the ordinate indicates the changes of the urban daytie population as a result of changes in k, and the value ranges of A is fro 4% to 65% (that values are close to the population ratio of day and night population in Chiyoda District of Tokyo and Luwan District of Shanghai, respectively). With the increase of k, x gradually becoes saller. Thus decrease the proportion of residential population and increase the population ratio of day and night, which could increase the capacity of urban daytie population. The above nuerical siulation results indicate there are

4 4 Shiqing Yan: Nonlinear Dynaic Analysis of Urban Roads and Daytie Population two easures to increase the capacity of urban daytie population, (i) By iproving the efficiency of urban transport systes, reduce the travel intensity of couters A and B. In the real world, Beijing take the Two-axis, two-belt, ulti-center space developent strategy and construct Metro line 0 and line 6 through the CBD [4], which reduce the urban traffic pressure by reducing the aount of travel of couter population. (ii) By reducing the proportion of residential population in the daytie population k, and the decreasing the aount of travel of residential population and reducing urban traffic pressure. For instance, the density of night population in Tokyo, New York and other international etropolitan are saller than in Shanghai and Beijing, so the traffic pressure is relatively sall [5].... The Relationship Between the Total Area of Urban Road y and the Maxiu Road Area that a City Can Afford y y is the axiu road area that a city can afford, when the traffic deands are sae, the larger the axiu nuber of roads that a city can afford, the larger the area of road. In order to study the relationship between the, we set the through capacity of road a( Ak + Bk + Ck) as constant, and nuerical siulation result as show in figure. road area of a city, and the value ranges of a( Ak + Bk + Ck) is fro % to 60%. Different fro figure and figure, fro figure we can see that y becoes larger with the increase of y. When the traffic deand is fixed, y liit the change of y. In reality, it is easier to increase road areas in suburbs and rural than in city center, so the per capita road area in suburbs and rural is uch larger than in city. Therefore, traffic congestion occurs ainly in the urban core area and the focus of traffic anageent should also be in the city core area. 4. Soe Suggestions to Urban Planning Through the discussion of the equilibriu state N, it can be obtained the relationship between the urban road area, the urban daytie population and the trip intensity, and it has soe enlightenent to the urban planning. 4.. Urban Daytie Population Must Maintain Moderate Growth And should be saller than4 R( Ak + Bk + Ck)/ y. If the urban daytie population growth too fast, it will be disadvantageous to the stability of the urban population and the road syste. And then it ay lead to urban congestion and have a negative ipact on the econoic and social developent of city. Especially in the central areas of large cities, they should control the growth of daytie population. 4.. The Urban Daytie Population Is Proportional to the Road Area at Steady State Figure. The relationship between the road area in a city and the axiu road area the city can bear. Where the solid line ( y ), dot line ( y ), dash line ( y ) and dash dot line ( y 4) are corresponding to four conditions of ab taking the nuber of 0., 0.4, 0.6 and 0.8, respectively. Figure shows when a( Ak + Bk + Ck) is constant, the relationship between the road area y and the axiu road area that a city can afford y. Abscissa y is the axiu road area that a city can bear, the ordinate y indicates the i. Strengthen the anageent of urban road traffic, iprove the carrying capacity of per unit road area, and then increase the nuber of urban daytie population. ii. In the forulation of urban developent plans, not only to consider the total population of a city, but also should take into account urban planning progras, econoic developent speed, industrial structure changes, CBD function enhanceents and other factors that ay ipact on urban daytie population and its traffic deand. According to the principle of appropriate advance, rational planning of urban road land. iii. Coordinate the relationship between road area and traffic deand. In the urban planning process, the difference of the nuber of daytie population, travel intensity and road capacity in different areas of the city should be considered, to avoid traffic congestion due to excessive concentration of daytie traffic deand in soe areas. In order to reduce the pressure of the urban traffic that generated by the urban econoic developent, the urban core area with concentrated daytie population ay be suitable for developing industries with sall daytie traffic deand. In urban anageent, institutions should stagger the work tie and get off tie to reduce traffic flow during peak hours, to avoid traffic congestion.

5 Urban and Regional Planning 07; (): The Growth of Urban Road Area Is Subject to the Maxiu Road Area the City Can Bear i) In the process of urban planning, we ust consider the spatial difference of urban road growth rate. Different cities and different regions of the city, the road area growth rates are different because the axiu nubers of roads they can bear are different. Widening or constructing new roads, it is ore difficult for the large cities than the ediu-sized cities, sall towns and it is ore difficult for the central areas than the suburbs. ii) The relationship and changes between the traffic deand generated by daytie population and the urban road area affect the structure of urban traffic syste and its changes. In space, different sizes of cities and different regions of the city, the structure of the transport syste and its developent directions are different. In large cities and the city's central areas, where are difficult to increase road area and per capita road area are relatively sall, private transport with low road use efficiency should be restricted and actively develop public transport with high road utilization rate. The suburbs and sall towns in large cities, due to both the daytie population and the traffic deand are sall, it is difficult to develop public transport, so it should actively develop private transport with good accessibility. In tie, there is an evolutionary process of urban traffic structure. With the developent of the city, the probability of increasing the road area in the sae area is getting saller and saller, the per capita road area is decreasing gradually, and the transportation syste should be developed fro private traffic to public transportation In a Certain Road Passing Capacity, the Capacity of Urban Daytie Population Is Inversely Proportional to the Travel Intensity of Daytie Population i) In urban transport planning, the radial road syste shortens the distance to the central area of the city, and then reduces the aount of people traveling, thus reducing road traffic pressure. Based on this reason, in the traffic developent and construction planning, during the th five-year plan period, Beijing city constructed a nuber of radial rail transits. ii) In urban spatial layout, to avoid the function of the city is too concentrated. Single-core etropolitan increase the distance of the couter population to reach the city center, and bring great pressure to urban traffic, so this layout should be adjusted. Construct coercial and residential areas in the city center can reduce the travel aount of CBD staffs. Residential areas equipped with public facilities to eet the basic aterial and cultural life of the residents, which can reduce the nuber of trips, travel distance and then reduce the travel intensity. iii) In the aspect of transportation ode, we draw lessons fro the city layout pattern that oriented by public transportation. To attract residents to use public transport, reduce the road area occupied by residents travel, and then reduce the travel volue of daytie population. Doestic and international actual results show that the construction of public transport counity can effectively reduce the traffic volue of vehicles within the counity [7-9]. iv) Appropriately reduce the proportion of the residential population in the urban center area, which can increase the capacity of daytie population and ease urban traffic pressure. Strengthen the study of the urban functional areas and separation of work places and residential places, and relocate appropriately the city's residential function. Optiize the industrial structure in the central area of the city, develop the deep functions of the CBD, protect the ecological environent and historical and cultural landscape in the central area of the city, develop the touris resources and develop the odern service industry, so that the city center area truly becoe the core of the city and the power of urban expansion [0]. Concentrating a large nuber of high-quality daytie working population, attracting ore non-working people to shopping, touris, consulting and so on, and then reduce the proportion of the residential population in the urban center. Iprove the ratio of day and night population in city center area, and ease urban traffic pressure. Soe people worry that this will cause of the epty city phenoenon in the central city. In fact, at present the ratio of day and night population in the central city of China is lower than in western international etropolis, by increasing the ratio of day and night population to ease the traffic pressure in the urban center has great potential []. 5. Conclusions Based on nonlinear dynaics theory, this paper analyzes the relationship between the area of urban road and the daytie population. The author constructs the nonlinear dynaics odel of the urban road and the daytie population, and calculates the equilibriu state of the dynaics syste. Besides, through the discussion of the equilibriu state this paper gets the relationship between the urban road area, the urban daytie population and the trip intensity. The results show that the nuber of urban daytie population is proportional to the area of urban road at steady state. The author also finds that the increase of urban road area is constrained by the axiu road area of a particular area at the city. When the road area is fixed, the nuber of urban daytie population is inversely proportional to the travel intensity. Furtherore, this paper provides soe suggestions to the urban planning. Acknowledge This research was supported by the project of philosophy and social science research in colleges and universities in Jiangsu province No. 06SJB8400.

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