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## A mathematical analysis for the forecast research on tourism carrying capacity to promote the effective and sustainable development of tourism

 Business School, Sichuan University, Chengdu, Sichuan 610064, China

* Corresponding author: Xiaowen Jie, jiexw@vip.163.com

Received  September 2017 Revised  December 2017 Published  November 2018

With the continuous and quick development of Chinese tourism industry over years, ecological environmental problems emerge consequently. The contradiction between the development of tourism economy and the protection of ecological environment has become the focus of scientific experts and Chinese government, and accordingly it is of vital importance to predict tourism carrying capacity accurately. In this paper, a new forecast approach is proposed for government staff and scenic spot management staff on tourist carrying capacity, which promotes the effective, healthy and sustainable development of the tourism country.

Citation: Yanan Wang, Tao Xie, Xiaowen Jie. A mathematical analysis for the forecast research on tourism carrying capacity to promote the effective and sustainable development of tourism. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2019056
##### References:
 [1] G. E. P. Box and G. M. Jenkins, Time series analysis, forecasting and control, San Francisco: Holden Day, 1970. [2] A. Carreño, A. Vidal-Ferrándiz, D. Ginestar and G. Verdú, Multilevel method to compute the lambda modes of the neutron diffusion equation, Applied Mathematics and Nonlinear Sciences, 2 (2017), 225-236. [3] F. Chan, C. Lim and M. McAleer, Modelling multivariate international tourism demand and volatility, Tourism Management, 26 (2005), 459-471. [4] V. Cho, Tourism forecasting and its relationship with leading economic indicators, Journal of Hospitality and Tourism Research, 25 (2001), 399-420. [5] Y. Deng, etal, The processing of boundary problem in EMD method and Hilbert transform, Chinese Science Bulletin, 46 (2001), 257-263. [6] J. Gao, Principle of artificial neural network and simulation example, Beijing: China Machine Press, 2003, 1-2. [7] C. Goh and R. Law, Modeling and forecasting tourism demand for arrivals with stochastic nonstationary seasonality and intervention, Tourism Management, 23 (2002), 499-510. [8] W. Guo and J. Li, Tourism demand prediction based on improved optimized combined method, Statistics and Decision, 8 (2011), 75-77. [9] X. Guo and L. Wang, New algorithm and application of empirical mode decomposition, Noise and Vibration Prediction, 5 (2008), 70-71. [10] N. Huang, etal, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non - stationary time series analysis, Proceedings of the Royal Society of London, 454 (1998), 903-995. doi: 10.1098/rspa.1998.0193. [11] N. Kulendran and K. Wilson, Modelling business travel, Tourism Economics, 6 (2000), 47-59. [12] N. Kulendran and S. F. & Witt, Leading indicator tourism forecasts, Tourism Management, 24 (2003b), 503-510. [13] R. Law, A neural network model to forecast Japanese demand for travel to Hong Kong, Tourism Management, 20 (1999), 89-97. [14] K. Lei and Y. Chen, Chinese inbound tourist capacity prediction based on bp neural network and arima combined model, Tourism Tribune, 22 (2007), 20-25. [15] K. Lei and Y. Chen, Prediction of chinese inbound tourist capacity based on bp neural network and ARIMA combined model, Tourism Tribune, 22 (2007), 20-25. [16] G. Li, K. F. Wong, H. Song and S. F. Witt, Tourism demand forecasting: A time varying parameter error correction model, Journal of Travel Research, 45 (2006), 175-185. [17] C. Lim and M. McAleer, Cointegration analysis of quarterly tourism demand by Hong Kong and Singapore for Australia, Applied Economics, 33 (2001a), 1599-1619. [18] X. Liu, Improvement and Application of BP Algorithm, Taiyuan: Taiyuan University of Technology, 2012. [19] H. Liu, etal, Empirical mode decomposition method and its implementation, Computer Engineering and Applications, 32 (2006), 44-47. [20] M. Rosa and M. L. Gandarias, Multiplier method and exact solutions for a density dependen reaction-diffusion equation, Applied Mathematics and Nonlinear Sciences, 1 (2016), 311-320. [21] J. Shan and K. Wilson, Causality between trade and tourism: Empirical evidence from China, Applied Economics Letters, 8 (2001), 279-283. [22] E. Smeral and M. Wuger, Does complexity matter? Methods for improving forecasting accuracy in tourism: The case of Australia D, Journal of Travel Research, 44 (2005), 100-110. [23] H. Song and G. Li., Tourism demand modelling and forecasting—A review of recent research, Tourism Management, 29 (2008), 203-220. [24] H. Song and S. F. Witt, Forecasting international tourist flows to Macau, Tourism Management, 27 (2006), 214-224. [25] H. Song, S. F. Witt and T. C. Jensen, Tourism forecasting: Accuracy of alternative econometric models, International Journal of Forecasting, 19 (2003), 123-141. [26] H. Song, K. K. F. Wong and K. K. S. Chon, Modelling and forecasting the demand for Hong Kong tourism, International Journal of Hospitality Management, 22 (2003), 435-451. [27] J. Song, etal, Simulation model verification method based on empirical mode decomposition and gray relational analysis, Systems Engineering and Electronics, 35 (2013), 2613-2618. [28] W. Tao and M. Ni, A comparative study of tourism demand prediction in china and the west: Theoretical basis and model, Tourism Tribune, 8 (2010), 12-16. [29] C. Tideswell, T. Mules and B. Faulkner, An integrative approach to tourism forecasting: A glance in the rearview mirror, Journal of Travel Research, 40 (2001), 162-171. [30] Y. Wang, F. Li and Y. Zhang, et al., Prediction of Long-term Tourist Capacity in Wulong Scenic Spot Based on Combined Model, Mathematical Statistics and Management, 30 (2011), 770-779. [31] F. Wang and W. Zheng, A study of chinese international inbound tourism demand fluctuation based on ARIMA and GARCH, Industrial Economy, 7 (2009), 53-57. [32] W. Yu and C. Mu, Forecasting the short-term metro passenger flow with empirical mode decomposition and neural networks, Transportation Research, 2012, 152-154. [33] X. Zhao, L. Wang and H. Zou, Overview of prediction methods of international tourism demand in tourist destination countries, Tourism Tribune, 6 (1996), 27-29.

show all references

##### References:
 [1] G. E. P. Box and G. M. Jenkins, Time series analysis, forecasting and control, San Francisco: Holden Day, 1970. [2] A. Carreño, A. Vidal-Ferrándiz, D. Ginestar and G. Verdú, Multilevel method to compute the lambda modes of the neutron diffusion equation, Applied Mathematics and Nonlinear Sciences, 2 (2017), 225-236. [3] F. Chan, C. Lim and M. McAleer, Modelling multivariate international tourism demand and volatility, Tourism Management, 26 (2005), 459-471. [4] V. Cho, Tourism forecasting and its relationship with leading economic indicators, Journal of Hospitality and Tourism Research, 25 (2001), 399-420. [5] Y. Deng, etal, The processing of boundary problem in EMD method and Hilbert transform, Chinese Science Bulletin, 46 (2001), 257-263. [6] J. Gao, Principle of artificial neural network and simulation example, Beijing: China Machine Press, 2003, 1-2. [7] C. Goh and R. Law, Modeling and forecasting tourism demand for arrivals with stochastic nonstationary seasonality and intervention, Tourism Management, 23 (2002), 499-510. [8] W. Guo and J. Li, Tourism demand prediction based on improved optimized combined method, Statistics and Decision, 8 (2011), 75-77. [9] X. Guo and L. Wang, New algorithm and application of empirical mode decomposition, Noise and Vibration Prediction, 5 (2008), 70-71. [10] N. Huang, etal, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non - stationary time series analysis, Proceedings of the Royal Society of London, 454 (1998), 903-995. doi: 10.1098/rspa.1998.0193. [11] N. Kulendran and K. Wilson, Modelling business travel, Tourism Economics, 6 (2000), 47-59. [12] N. Kulendran and S. F. & Witt, Leading indicator tourism forecasts, Tourism Management, 24 (2003b), 503-510. [13] R. Law, A neural network model to forecast Japanese demand for travel to Hong Kong, Tourism Management, 20 (1999), 89-97. [14] K. Lei and Y. Chen, Chinese inbound tourist capacity prediction based on bp neural network and arima combined model, Tourism Tribune, 22 (2007), 20-25. [15] K. Lei and Y. Chen, Prediction of chinese inbound tourist capacity based on bp neural network and ARIMA combined model, Tourism Tribune, 22 (2007), 20-25. [16] G. Li, K. F. Wong, H. Song and S. F. Witt, Tourism demand forecasting: A time varying parameter error correction model, Journal of Travel Research, 45 (2006), 175-185. [17] C. Lim and M. McAleer, Cointegration analysis of quarterly tourism demand by Hong Kong and Singapore for Australia, Applied Economics, 33 (2001a), 1599-1619. [18] X. Liu, Improvement and Application of BP Algorithm, Taiyuan: Taiyuan University of Technology, 2012. [19] H. Liu, etal, Empirical mode decomposition method and its implementation, Computer Engineering and Applications, 32 (2006), 44-47. [20] M. Rosa and M. L. Gandarias, Multiplier method and exact solutions for a density dependen reaction-diffusion equation, Applied Mathematics and Nonlinear Sciences, 1 (2016), 311-320. [21] J. Shan and K. Wilson, Causality between trade and tourism: Empirical evidence from China, Applied Economics Letters, 8 (2001), 279-283. [22] E. Smeral and M. Wuger, Does complexity matter? Methods for improving forecasting accuracy in tourism: The case of Australia D, Journal of Travel Research, 44 (2005), 100-110. [23] H. Song and G. Li., Tourism demand modelling and forecasting—A review of recent research, Tourism Management, 29 (2008), 203-220. [24] H. Song and S. F. Witt, Forecasting international tourist flows to Macau, Tourism Management, 27 (2006), 214-224. [25] H. Song, S. F. Witt and T. C. Jensen, Tourism forecasting: Accuracy of alternative econometric models, International Journal of Forecasting, 19 (2003), 123-141. [26] H. Song, K. K. F. Wong and K. K. S. Chon, Modelling and forecasting the demand for Hong Kong tourism, International Journal of Hospitality Management, 22 (2003), 435-451. [27] J. Song, etal, Simulation model verification method based on empirical mode decomposition and gray relational analysis, Systems Engineering and Electronics, 35 (2013), 2613-2618. [28] W. Tao and M. Ni, A comparative study of tourism demand prediction in china and the west: Theoretical basis and model, Tourism Tribune, 8 (2010), 12-16. [29] C. Tideswell, T. Mules and B. Faulkner, An integrative approach to tourism forecasting: A glance in the rearview mirror, Journal of Travel Research, 40 (2001), 162-171. [30] Y. Wang, F. Li and Y. Zhang, et al., Prediction of Long-term Tourist Capacity in Wulong Scenic Spot Based on Combined Model, Mathematical Statistics and Management, 30 (2011), 770-779. [31] F. Wang and W. Zheng, A study of chinese international inbound tourism demand fluctuation based on ARIMA and GARCH, Industrial Economy, 7 (2009), 53-57. [32] W. Yu and C. Mu, Forecasting the short-term metro passenger flow with empirical mode decomposition and neural networks, Transportation Research, 2012, 152-154. [33] X. Zhao, L. Wang and H. Zou, Overview of prediction methods of international tourism demand in tourist destination countries, Tourism Tribune, 6 (1996), 27-29.
Schematic diagram of the combinatorial model based on empirical modal decomposition- error backpropagation artificial neural network
Structure map of error backpropagation of artificial neural network
2010 Mount Emei tourist area daily visitors capacity of the time series data
Comparison between the estimated value and the actual value of the tourism carrying capacity using the empirical modal decomposition-error backpropagation
Estimation error comparison between the empirical modal decomposition - error backpropagation artificial neural network prediction model and single error backpropagation artificial neural network prediction model
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