The System Dynamics Numerical Simulation Of Airline Dynamic Game With Multidimensional Parameters

The numerical simulation methods are used in this paper to study the local and global dynamics of airline dynamic game system under nonlinear variable costs.It is interest of focusing on the influence of the parameters on the dynamic evolution law of airline dynamic game system,such as the adjustment speed,the price sensitivity coefficient,the marginal cost,etc.The main contents of this paper are given as follows:1.Based on the assumption of nonlinear variable cost function,an airline dynamic bidding game under multi-dimensional parameter system is established.The existence and stability conditions of four equilibrium points are theoretically analyzed.By using the numerical simulation method,the stability of the equilibrium points and the complex dynamic behaviors of the system after losing stability are verified.The path dependence of the system are numerically simulated with the attractors and the basin of attraction.The causes of "holes" and "gap" appearing in the basin of attraction are analyzed with the help of noninvertible map and the critical curves.In addition,the dynamic behaviors under two cases that symmetric information and asymmetric information are discussed,and it is found that the fractal structures,such as Arnol'd tongues,are widely existed in the parameter space of the system.2.Taking the airline output as the decision parameter,an airline dynamic output game under multi-dimensional parameter system is established.The existence conditions and stability conditions of the four equilibrium points are theoretically analyzed in the economic sense,and the stability region and bifurcation conditions of the Nash equilibrium point are given.Using the method of numerical simulation,the complex dynamic behaviors after the instability of the Nash equilibrium point and the path to chaos in the two-parameter space can be showed.With the help of the single-parameter bifurcation diagram and the largest Lyapunov exponent diagram,the phenomenon of "jumping" appearing on the bifurcation pathway are studied and it is found that there are multiple attractors coexisting in basin of attraction.Then the basin of attraction of the system can be drawn basing on the cell mapping algorithm.The dynamic evolutions of the topological structure of the attractor and basin of the system under symmetric and asymmetric information are discussed.3.Combining price competition with output competition,an airline dynamic hybrid game under multi-parameter system is established.The stability conditions of the Nash equilibrium point and the boundary equilibrium points are theoretically analyzed.The stability region and dynamic complexity after instability are simulated through numerical simulation.The reason why the "hole" appears in the basin of attraction is analyzed with the help of the critical curves and noninvertible map.The dynamic behavior of the system under symmetrical information is numerically simulated,and the influences of its own price-sensitive parameters and cross-price sensitivity coefficients on the system dynamic behaviors and aviation companies' decision-making are analyzed.The evolution of topological structure of the basin of attraction with the parameters changing is discussed,which may reveal the formation mechanism of the "hole" in the basin of attraction.4.The non-smooth dynamic system of airline dynamic price game when profit is a piecewise function is established.The existence conditions and stability conditions of the equilibrium points of the non-smooth dynamics model are theoretically analyzed.The complex dynamic phenomena of the system after the equilibrium point loses stability,such as bifurcation,chaos and escaping behaviors,are numerically characterized.It is found that there are some unique bifurcation types in non-smooth dynamic system,such as periodic bifurcation.