The Research Of Upstream And Downstream Project Portfolio Risk System Based On The Interaction Effect

With the increasingly fierce market competition,project portfolio has become a common behavior that the enterprise enhance their competitiveness and effectively avoid risks.Upstream and downstream project portfolio is an important combination.Taking into account the risk of the project portfolio will be affected by constant support,time lag,interactive effects and other complex factors.In this paper,based on the theory of predator-prey system,project portfolio risk system with constant support and time delay is established and studied.Firstly,the two-item portfolio risk system with constant support is built under the interaction effect.The sufficient conditions for the two projects to coexist persistently are obtained,and the global stability of portfolio risk is studied.Finally,the trajectory of the project risk with time is obtained by numerical simulation.It is verified that the risk of the combination is obviously lower than the risk before the combination when the parameters meet certain conditions.Through this method,manager can analyze the influence of the constant support and interaction between the project to the portfolio risk,and the ability of enterprises to resist risks can be improve.Secondly,the risk system of two and three projects with time delay is constructed.The local stability and Hopf bifurcation of system risk are discussed,using the Hopf bifurcation theory to obtain the critical ? value of the combination risk stability and instability,the formulas of the change direction of the risk and the periodicity changes of the risk when the risk is unstable with the time delay as the parameter.And the sufficient condition for the global stability of the system risk is obtained.Numerical simulation is carried out to validate the correctness of the conclusions,and obtain the trajectory diagram of the project risk with time changes,and the change trend chart when the project risk is unstable.Through this method,the manager can analyze the trend of the project risk when the time lag and the interaction effect meet the different conditions,and then more effectively control the risk.In this paper studies three types of Upstream and downstream portfolio risk systems based on interaction effects.From the previous single point of time research to the continuous point of time to study,to expand the biological mathematics in the project portfolio risk research applications.At the same time,a theoretical basis is provided for managers to analyze the influence of complex factors such as constant support and time lag on portfolio risk.