Abstract
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.
Similar content being viewed by others
References
Mohr, J., Spekman, R.: Characteristics of partnership success: partnership attributes, communication behavior, and conflict resolution techniques. Strateg. Manag. J. 15(2), 135–152 (1994)
Kale, P., Singh, H.: Building firm capabilities through learning: the role of the alliance learning process in alliance capability and firm-level alliance success. Strateg. Dir. 28(2), 981–1000 (2008)
Schreiner, M., Kale, P., Corsten, D.: What really is management capability and how does it impact alliance outcomes and success. Strateg. Manag. J. 30(13), 1395–1419 (2009)
Mazouz, B., Facal, J., Viola, J.: Public-private partnership: elements for a project-based management typology. Project Manag. J. 39(2), 98–110 (2008)
Davila, A., Foster, G., Gupta, M.: Venture capital financing and the growth of startup firms. J. Bus. Ventur. 18(6), 689–708 (2003)
Magri, S.: The financing of small innovative firms: the Italian case. Econ. Innov. New Technol. 18(2), 181–204 (2009)
Rin, M., Hellmann, T., Puri, M.: A survey of venture capital research. Soc. Sci. Electron. Publ. 2(Part A), 573–648 (2013)
Lin, L., Yuan, G., Wang, H., Xie, J.: The stochastic incentive effect of venture capital in partnership systems with the asymmetric bistable CobbDouglas utility. Commun. Nonlinear Sci. Numer. Simul, 66, 109–128 (2019)
Benzi, R., Sutera, A., Vulpiani, A.: The mechanism of stochastic resonance. J. Phys. A Math. Gen. 14, L453–L457 (1981)
Stocks, N., Stein, N., McClintock, P.: Stochastic resonance in monostable systems. J. Phys. A Gener. Phys. 26(7), L385–L390 (1993)
Evstigneev, M., Reimann, P., Pankov, V., Prince, R.: Stochastic resonance in monostable overdamped systems. Europhys. Lett. 65(1), 7–12 (2004)
Agudov, N., Krichigin, A.: Stochastic resonance and antiresonance in monostable systems. Radiophys. Quantum Electron. 51(1), 812–824 (2008)
Repullo, R., Suarez, J.: Venture capital finance: a security design approach. Rev. Finance 8(1), 75–108 (1999)
Mandal, P., Garai, A., Roy, T.: Cobb-Douglas based firm production model under fuzzy environment and its solution using geometric programming. Appl. Appl. Math. 11(1), 469–488 (2016)
Vilar, J., Rubi, J.: Divergent signal-to-noise ratio and stochastic resonance in monostable systems. Phys. Rev. Lett. 77(14), 2863–2866 (2010)
Guo, F., Luo, X., Li, S., Zhou, Y.: Stochastic resonance in a monostable system driven by square-wave signal and dichotomous noise. Chin. Phys. B 19(8), 080504 (2010)
Leng, Y., Zhao, Y.: Pulse response of a monostable system. Acta Phys. Sin. 64(21), 210503 (2015)
Raikher, Y., Stepanov, V.: Stochastic resonance and phase shifts in super paramagnetic particles. Phys. Rev. B 52(5), 3493–3498 (1995)
Khovanov, I., Poloinkin, A., Luchinsky, D., Mcclintock, P.: Noise-induced escape in an excitable system. Phys. Rev. E 87(3), 032116 (2013)
Zhang, W., Xiang, B.: A new single-well potential stochastic resonance algorithm to detect the weak signal. Talanta 70(2), 267–271 (2006)
Lin, L., Wang, H., Lv, W., Zhong, S.: A novel parameter-induced stochastic resonance phenomena in fractional Fourier domain. Mech. Syst. Signal Process. 76–77, 771–779 (2016)
Younesian, D., Jafari, A., Serajian, R.: Effect of the bogie and body inertia on the nonlinear wheel-set hunting recognized by the Hopf bifurcation theory. Int. J. Autom. Eng. 1(3), 186–196 (2011)
Serajian, R.: Parameters’ changing influence with different lateral stiffnesses on nonlinear analysis of hunting behavior of a bogie. J. Vibroeng. 1(4), 195–206 (2013)
Luo, X., Guo, F., Zhou, Y.: Stochastic resonance in an asymmetric monostable system subject to two periodic forces and multiplicative and additive noise. Commun. Theor. Phys. 51, 283–286 (2009)
Agudov, N., Krichigin, A., Valenti, D., Spagnolo, B.: Stochastic resonance in a trapping overdamped monostable system. Phys. Rev. E 81(1), 051123 (2010)
Yao, M., Xu, W., Ning, L.: Stochastic resonance in a bias monostable system driven by a periodic rectangular signal and uncorrelated noises. Nonlinear Dyn. 67(1), 329–333 (2012)
Arathi, S., Rajasekar, S.: Stochastic resonance in a single-well anharmonic oscillator with coexisting attractors. Commun. Nonlinear Numer. Simul. 19(12), 4049–4056 (2014)
Duan, C., Zhan, Y.: The response of a linear monostable system and its application in parameters estimation for PSK signals. Phys. Lett. A 380(14–15), 1358–1362 (2016)
Comin, D.: Total factor productivity. Organ. Environ. 19(1), 171–190 (2008)
Lappalainen, J., Niskanen, M.: Financial performance of SMEs: impact of ownership structure and board composition. Manag. Res. Rev. 35(11), 1088–1108 (2012)
Kortenkamp, K., Moore, C.: Time, uncertainty, and individual differences in decisions to cooperate in resource dilemmas. Personal. Soc. Psychol. Bull. 32(5), 603–615 (2006)
Choi, S., Lee, C., Jr, R.: Corporate social responsibility performance and information asymmetry. J. Acc. Public Policy 32(1), 71–83 (2013)
Michaels, A., Gr\(\ddot{\rm u}\)ning, M.: Relationship of corporate social responsibility disclosure on information asymmetry and the cost of capital. J. Manag. Control 28(3), 251–274 (2017)
Reichl, L.: A Modern Course in Statistical Physics, 3rd edn. Wiley, Hoboken (2016)
Risken, H.: The Fokker-Planck Equation. Methods of Solution and Applications. Springer, Berlin (1984)
Li, J.: Effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean-field coupling. Phys. Rev. E 66(3pt1), 031104 (2002)
Hu, G., Haken, H., Ning, C.: Nonlinear-response effects in stochastic resonance. Phys. Rev. E 47(4), 2321–2325 (1993)
Anishchenko, V., Astakhov, V., Vadivasova, T., Neiman, A., Schimansky-Geier, L.: Nonlinear Dynamics of Chaotic and Stochastic Systems, 2nd edn. Springer, Berlin (2007)
Dubkov, A., Malakhov, A., Saichev, A.: Correlation time and structure of the correlation function of nonlinear equilibrium brownian motion in arbitrary-shaped potential wells. Radiophys. Quantum Electron. 43(4), 335–346 (2000)
Bali, T., Cakici, N., Chabi-Yo, F.: A generalized measure of riskiness. Manag. Sci. 57(8), 1406–1423 (2011)
Graf, S., Haertel, L.: The impact of inflation risk on financial planning and risk-return profiles. Astin Bull. 44(2), 335–365 (2014)
Hitchner, J.: Financial Valuation : Applications and Models, 3rd edn. Wiley, London (2010)
McNamara, B., Wiesenfeld, K.: Theory of stochastic resonance. Phys. Rev. A 39(9), 4854–4869 (1989)
Li, Q., Wang, T., Leng, Y., Wang, G.: Engineering signal processing based on adaptive step-changed stochastic resonance. Mech. Syst. Signal Process. 21(5), 2267–2279 (2007)
Lai, Z., Leng, Y., Sun, J., Fan, S.: Weak characteristic signal detection based on scale transformation of Duffing oscillator. Acta Phys. Sin. 61(5), 050503 (2012)
Zhang, G., Song, Y., Zhang, T.: Stochastic resonance in a single-well system with exponential potential driven by levy noise. Chin. J. Phys. 55(1), 85–95 (2017)
Dybiec, B.: Levy noises: double stochastic resonance in a single-well potential. Phys. Rev. E 80(4pt1), 041111 (2009)
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, L., Wang, H., Lin, L. et al. The incentive effect of venture capital in bilateral partnership systems with the bias mono-stable Cobb–Douglas utility. Nonlinear Dyn 95, 3127–3147 (2019). https://doi.org/10.1007/s11071-018-04745-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-018-04745-1