The incentive effect of venture capital in bilateral partnership systems with the bias mono-stable Cobb–Douglas utility

  • Lei Yu
  • Huiqi WangEmail author
  • Lifeng Lin
  • Suchuan Zhong
Original Paper


Partnerships, between multiple sides that share goals and strive for mutual benefit, are ubiquitous both between and within the enterprises, and competition and cooperation are the fundamental characteristics in partnership systems. As the inherent effect of capital-product switching applied together with stochastic fluctuations of internal and external environments, the effects compete and cooperate to make the system achieve global optimum in the statistical sense. Thus motivated, we establish an over-damped nonlinear Langevin equation to describe the dynamical behaviors subject to the bias mono-stable Cobb–Douglas utility under the wealth-constraint condition. Based on linear response theory, we derive the performance indexes, including output signal-to-noise ratio, stationary unit risk return, systematic risk and bilateral risk, and stochastic resonance (SR) and reverse SR phenomena are observed by the simulations. Finally, we introduce one true example to explain the actual phenomenon observed from the practice. The purpose in this paper is to develop a quantitative method and associated prototype system beg the questions of how the external venture capital incents the partners especially associated with partnership success and what roles the internal and external risks play, respectively.


Stochastic resonance (SR) Reverse stochastic resonance (RSR) Bias mono-stable nonlinear system Cobb–Douglas utility (CDU) potential Linear response theory (LRT) 



We would like to express our sincere appreciation and gratitude to the three anonymous reviewers and editor for their patience and constructive comments. This research is sponsored by the National Natural Science Foundation of China (11501386, 11701086), the Basic and Cutting-edge Research Program of Chongqing (cstc2017jcyjAX0412, cstc2017jcyjAX0106), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ1600306) and the Natural Science Foundation of Fujian Province (2017J01550). Also special thanks should go to Prof. Hong Ma, Prof. George Xianzhi Yuan, Prof. Shilong Gao and BBD Inc. for the help in providing actual SMEs data from manufacturing industry in China.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Computer and Information ScienceChongqing Normal UniversityChongqingChina
  2. 2.College of Mathematics and StatisticsChongqing UniversityChongqingChina
  3. 3.College of Computer and Information ScienceFujian Agriculture and Forestry UniversityFuzhouChina
  4. 4.School of Aeronautics and AstronauticsSichuan UniversityChengduChina

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