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This paper presents a study of the dynamic complexity of the Transmission Control Protocol (TCP) over mobile connections in the Universal Mobile Telecommunications System (UMTS) network. Using the concept of time-dependent exponent curves, the dynamic characteristics of TCP are studied and analysed from a simulation model of the UMTS network. Time-dependent exponent graphs have been used to test for chaotic behaviour in the traffic flow of wired communication networks. This paper fills the gap of studying the behavioural characteristics of TCP traffic flow inside the wireless UMTS network and additionally underlines the impact of this behaviour on the Quality of Service (QoS) offered by the network. An analysis of the results validates the existence of chaotic and random dynamics inside the traffic profile of the network. It is shown that in relation to traffic load, TCP exhibits from periodic to chaotic behaviour with relative levels of stochasticity. Based on these dynamics, it is shown that the occurrence of chaos, severely affects the QoS in the network.