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The impact of R&D on GDP study based on grey delay Lotka-Volterra model

Shuhua Mao (Reliability Engineering Center, Wuhan University of technology, Wuhan, China)
Mingyun Gao (School of Science, Wuhan University of Technology, Wuhan, China)
Min Zhu (School of Science, Wuhan University of Technology, Wuhan, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 2 February 2015




The purpose of this paper is to elevate the accuracy when predicting the gross domestic product (GDP) on research and development (R&D) and to develop the grey delay Lotka-Volterra model.


Considering the lag effects between input in R&D and output in GDP, this paper estimated the delay value via grey delay relation analysis. Taking the delay into original Lotka-Volterra model and combining with the thought of grey theory and grey transform, the authors proposed grey delay Lotka-Volterra model, estimated the parameter of model and gave the discrete time analytic expression.


Collecting the actual data of R&D and GDP in Wuhan China from 1995 until 2008, this paper figure out that the delay between R&D and GDP was 2.625 year and found the dealy time would would gradually be reduced with the economy increasing.

Practical implications

Constructing the grey delay Lotka-Volterra model via above data, this paper shown that the precision was satisfactory when fitting the data of R&D and GDP. Comparing the forecasts with the actual data of GDP in Wuhan from 2009 until 2012, the error was small.

Social implications

The result shows that R&D and GDP would be both growing fast in future. Wuhan will become a city full of activity.


Considering the lag between R&D and GDP, this work estimated the delay value via a grey delay relation analysis and constructed a novel grey delay Lotka-Volterra model.



This work was supported by the National Natural Science Foundation of China (Grant No. 51479151), the General Education Program (GEP) Requirements in the Humanities and Social Sciences project (Grant No. 11YJC630155), the Fundamental Research Funds for the Central Universities project (Grant No. 2014-Ia-015), and the China Postdoctoral Science Foundation Special Foundation project (Grant No. 2013T60755).


Mao, S., Gao, M. and Zhu, M. (2015), "The impact of R&D on GDP study based on grey delay Lotka-Volterra model", Grey Systems: Theory and Application, Vol. 5 No. 1, pp. 74-88.



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