LAUSR

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.