The problem of self–similarity in various areas of science and technology has interested researchers for a long time. Packet losses result in an additional network traffic and, finally, ”congestions”. At high–speed of data transfer packet losses, expressed in portions of a per cent, lead to considerable information losses. It has been shown in numerous papers devoted to the research of network traffic that the abovementioned phenomena are related to the properties of the traffic self–similarity which is mainly caused by the TCP protocol behaviour. However to date models have not been offered which adequately describe the behaviour of the communication networks of information systems and which allow to apply the whole arsenal of classic methods of analyzing nonlinear dynamic systems. The paper suggests a new approach to analyzing the communication network behaviour of information systems with TCP protocol – considering them as nonlinear dynamic systems manifesting chaotic properties at certain values of parameters. Phase portrait of the system under study are built, Lyapunov exponents for different values of the main system parameters are calculated. Recommendations on designing and operating high-speed optical communication networks of information systems are suggested.
1. Computer Simulation of Chaotic Phenomena in High-Speed Communication Networks Haengmuk Cho, Alexander V. Karpukhin, Igor N. Kudryavtsev, Alexander V. Borisov, Dmitriy I. Gritsiv Korean Institute Of Information Technology, Journal of Korean Institute of Information Technology, Vol.11 No.3 2013.3, page(s): 113-122

We propose a new dynamical model for capture of irregular moons which identifies chaos as the essential feature responsible for initial temporary gravitational trapping within a planet's Hill sphere. The key point is that incoming potential satellites get trapped in chaotic orbits close to "sticky" KAM tori in the neighbourhood of the planet, possibly for very long times, so that the chaotic layer largely dictates the final orbital properties of captured moons.

Several families of irregular moons orbit the giant planets. These moons are thought to have been captured into planetocentric orbits after straying into a region in which the planet's gravitation dominates solar perturbations (the Hill sphere). This mechanism requires a source of dissipation, such as gas-drag, in order to make capture permanent. However, capture by gas-drag requires that particles remain inside the Hill sphere long enough for dissipation to be effective. Recently we have proposed that in the circular restricted three-body problem particles may become caught up in `sticky' chaotic layers which tends to prolong their sojourn within the planet's Hill sphere thereby assisting capture. Here we show that this mechanism survives perturbations due to the ellipticity of the planet's orbit. However, Monte Carlo simulations indicate that the planet's ability to capture moons decreases with increasing orbital eccentricity. At the actual Jupiter's orbital eccentricity, this effects in approximately an order of magnitude lower capture probability than estimated in the circular model. Eccentricities of planetary orbits in the Solar System are moderate but this is not necessarily the case for extrasolar planets which typically have rather eccentric orbits. Therefore, our findings suggest that these extrasolar planets are unlikely to have substantial populations of irregular moons.