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Urban gravity model based on cross-correlation function and Fourier analyses of spatio-temporal process

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  • Chen, Yanguang

Abstract

This paper is devoted to gaining a new insight into urban physics in the right perspective. The conventional urban gravity model based on Newton’s Law of Universal Gravitation is made into a new expression based on a cross-correlation function. Endowed with a time-lag parameter and time functions, the developed model can integrate temporal dimension into spatial process of cities. A pair of gravity spectra can be given for spatial interaction of any two cities with Fourier transform, and the series of attraction quantity are proved to be the average values of interaction volumes from the traditional model. The method is applied to four cities in China, illustrating how to employ the improved model to characterize the spatio-temporal process of urban interaction. The new gravity model reveals the relationship between the concept of energy and the notion of interaction, and suggests asymmetric interaction between cities, commonly observed in the real world.

Suggested Citation

  • Chen, Yanguang, 2009. "Urban gravity model based on cross-correlation function and Fourier analyses of spatio-temporal process," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 603-614.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:603-614
    DOI: 10.1016/j.chaos.2008.02.030
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    References listed on IDEAS

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    1. Chen, Yanguang & Zhou, Yixing, 2008. "Scaling laws and indications of self-organized criticality in urban systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 85-98.
    2. Lin, Yong & Ruan, Huo-Jun, 2006. "Maximal operators and Fourier transforms of self-similar measures," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 121-126.
    3. Anderson, James E, 1979. "A Theoretical Foundation for the Gravity Equation," American Economic Review, American Economic Association, vol. 69(1), pages 106-116, March.
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    Cited by:

    1. Zhangfeng Yao & Kunhui Ye & Liang Xiao & Xiaowei Wang, 2021. "Radiation Effect of Urban Agglomeration’s Transportation Network: Evidence from Chengdu–Chongqing Urban Agglomeration, China," Land, MDPI, vol. 10(5), pages 1-21, May.
    2. Chen, Yanguang, 2011. "Fractal systems of central places based on intermittency of space-filling," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 619-632.
    3. Chen, Yanguang, 2014. "An allometric scaling relation based on logistic growth of cities," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 65-77.
    4. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    5. Yanguang Chen, 2015. "A New Methodology of Spatial Cross-Correlation Analysis," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-20, May.
    6. Nir Kaplan & Itzhak Omer, 2022. "Multiscale Accessibility—A New Perspective of Space Structuration," Sustainability, MDPI, vol. 14(9), pages 1-19, April.
    7. Su, Kai & Yu, Qiang & Yue, Depeng & Zhang, Qibin & Yang, Lan & Liu, Zhili & Niu, Teng & Sun, Xiaoting, 2019. "Simulation of a forest-grass ecological network in a typical desert oasis based on multiple scenes," Ecological Modelling, Elsevier, vol. 413(C).
    8. Li He & Jian’ge Tao & Ping Meng & Dan Chen & Meng Yan & Lászlo Vasa, 2021. "Analysis of socio-economic spatial structure of urban agglomeration in China based on spatial gradient and clustering," Oeconomia Copernicana, Institute of Economic Research, vol. 12(3), pages 789-819, September.
    9. Chen, Yanguang, 2015. "The distance-decay function of geographical gravity model: Power law or exponential law?," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 174-189.
    10. Kai Zhu & Zhiling Gu & Jingang Li, 2023. "Analysis of the China’s Interprovincial Innovation Connection Network Based on Modified Gravity Model," Land, MDPI, vol. 12(5), pages 1-19, May.

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