Dynamic Gravity Model and Dynamic Behavior Analysis Based on Improved Cost Function

Abstract

This paper introduces a dynamic gravity model of O- D flows changing in discrete-time periods with dynamic characteristics of balance, oscillation, period doubling, and chaos. The original cost function only considers the traffic conditions when it flows freely. This leads to not matching the calculation results of the model and the actual traffic conditions. Therefore, the cost function was improved as follows: when congestion occurs, adding traffic reduction and road capacity is resultant as the traffic volume to the cost function; when obstruction occurs, the study sets a large value to the saturability in the cost function. At this point, the cost function is improved reflecting the three traffic conditions: free, congested, and obstructed. On this basis, the complex dynamic characteristics are found by applying the improved cost function to the double-constrained dynamic gravity model and analyzing the model through bifurcation diagrams, time series diagrams, maximum Lyapunov exponent spectrograms. Finally, by comparing the dynamics maps of the models, it is found that the improved model can easily recover to the periodic state after being disturbed and has stronger robustness and structural stability.