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It is well known that traffic systems are highly nonlinear. Previous research has shown the existence of the chaotic behavior in traffic flow data. However, the corresponding result in individual vehicle behavior has not been investigated. In this paper, we use tools of nonlinear time series analysis to explore the chaotic characteristic from data of individual vehicle behavior in car following. The maximal Lyapunov exponent and correlation dimension of these data are calculated numerically and compared with the results of traffic volume. The consistency of traffic flow and individual vehicle behavior is illustrated clearly from viewpoints of chaotic analysis.