| In this paper,based on Li-Du-Massar quantum scheme and gradient adjustment mechanism,dynamic models of supply chain quantum game considering service quality are established,and the stability of quantum equilibrium points of the system is analyzed by using stability theory.The local bifurcation and global dynamics of the system are studied using numerical simulation methods.The emphasis is placed on the complex dynamic behavior of the system after quantizing the initial model.The main contents of this paper are as follows:1.Based on the degree of service quality improvement of the service integrator and the service provider as decision strategies,a quantum game dynamic model is established,and its iterative property is used to simulate the dynamic evolution of economic systems.The stability of quantum equilibrium points of the system is analyzed by stability theory and the stability domain of the system is obtained.By means of bifurcation theory and 1-D bifurcation diagram,the dynamical behaviors of the system under the condition of quantum entanglement disappearing and quantum entanglement existing are compared.It is found that the introduction of quantum entanglement changes the non-cooperative relationship between the service integrator and the service provider in the dynamic market.Then,using the bifurcation diagrams,the influence of different parameters on the local stability of the system when the quantum entanglement is not zero is analyzed,and the conditions for maintaining the quantum Nash equilibrium state of the system are found.Finally,by drawing the basin of attraction,the global dynamic behavior of the system is studied.When the attractors contact the critical curves,the contact bifurcation is found.The jump points appearing in the local bifurcation analysis of the system are also found in the global dynamic behavior as the coexistence of multiple groups of attractors.The internal and external boundaries of the attractor are depicted by the critical curves.The chaos appearing in the system is a deterministic chaos,which is proved.2.Based on the degree of service quality effort of the service integrator and the service provider as decision strategies,a dynamic quantum game model of with quality preference level is established,and the stability conditions of four quantum equilibrium points are analyzed.By means of numerical simulation,the local and global dynamics of the system are studied.The results show that the bifurcation diagram shows that there are two paths causing the system to lose stability with the change of adjusting speed:flip bifurcation paths and Neimark-Sacker bifurcation paths.According to the changes of the corresponding attractors,the complex internal characteristics of the system in chaotic state are displayed,and the phenomenon of frequency locking is found.In addition,it is found that the smaller the quantum entanglement is,the more stable the system is when the adjustment speed of the service provider is unchanged,and many Arnold tongues are found in the 2-D bifurcation diagram,which is reflected in the fact that there are multiple"periodic windows"in the 1-D bifurcation diagram.It seems that chaos disappears in the periodic window,but in fact there is internal self-similarity of the system.Additionally,the complex bifurcation results in the emergence of"chaotic bubbles".Then,by drawing the profit bifurcation diagram and profit curve with quantum entanglement as the control parameter,it is found that the average quantum profit growth rate of the service integrator and the service provider decreases at the same time when the system bifurcation occurs.Finally,the initial value sensitivity of the system is analyzed by bifurcation diagram and basin of attraction,and it is found that different initial conditions will lead to the complete difference of the final state of the nonlinear dynamic system.3.Based on the degree of service quality of the service integrator and the service provider as decision strategies,a dynamic quantum game model of the service supply chain considering supervision level and quality expectation is established.The local stability of quantum equilibrium points is analyzed using stability theory,and the flip bifurcation curve or Neimark-Sacker bifurcation curve of the system is obtained.The effects of quantum entanglement and supervision level on the stability domain size of the service integrator and the service provider to maintain quantum Nash equilibrium and the probability of loss of stability through Neimark-Sacker bifurcation are studied by the bifurcation diagram.Then the attractors and time series of the system after crossing different bifurcation curves are drawn,and the attractors with different fractal structures caused by the system after going through two kinds of bifurcations are studied.It is found that the system can still maintain periodic stability after passing flip bifurcation.Using the 1-D bifurcation diagram and service quality curve,it is found that different parameters have different effects on system stability and service quality of the two enterprises.The multi-stable motion of the quantum game dynamic system is studied by means of the attractor and the basin of attraction.It is found that the escape domain is not in theZ0 region,which leads to the appearance of the hole in the basin of attraction,and leads to the complex boundary of the basin of attraction,which increases the pressure faced by enterprises when adjusting their strategies to a certain extent.At the same time,the hole boundary can be obtained by the iteration of basin of attraction boundary.Finally,the bifurcation diagram and profit curve are used to analyze the influence of system dynamics on the profits.It is concluded that when the system is maintained in the quantum Nash equilibrium state,not only can the stability of the service supply chain market be maintained,but also the service integrator and the service provider can obtain higher average quantum profits.It shows that the two enterprises can get the optimal result when they are in the state of quantum Nash equilibrium. |
