Chaos and self-similarity are the state-of-the-art problems in various areas of modern science and technology, thus network systems are not exception from this rule. Increasing number of various network protocols, applications and services leads to the fact that network traffic becomes more complex and unpredictable. It has been shown that phenomenon of self-similarity is caused by the properties of network traffic whose origin is the behavior of ТСР protocol. And all this properties became more significant with appearing of the high-speed data transmission technologies. Finally this behavior leads to congestion in network and packet losses as the result of it. But even modern congestion control mechanisms handle such kind of situations quite unfair. For example, as shown by W. Feng et al., TCP Reno loss rate exceeds 5% in a heavily congested network. So it’s easy to calculate that over a Gigabit Ethernet link such loss rate translates into a loss of over 50 Mb/s. Obviously this level of loss rate is unacceptable. However models that describe behavior of information systems sufficiently and give a possibility for scientists to apply all set of classical methods of chaos theory and analyze particular nonlinear dynamical system have not been offered so far. Phase portraits of the studied system were built and Lyapunov exponents for different values of the basic system parameters were calculated. In the present paper a new approach in analysis of the packet switching networks behavior with ТСР protocol is proposed. These networks are analyzed as nonlinear dynamical systems that show chaotic properties at a certain value of parameters.