Poincare reverse times in the interaction of chaotic and stochastic systems - Владимирський, Едуард Йосипович (Eastern-European Journal of Enterprise Technologies, 2012)
Nowadays there exists an urgent problem of analysis and forecasting of a great number of heterogeneous interacting information flows in complex structures. Information interactions are of dual nature of impact on the system and its environment. On the one hand, they act as a regulation mechanism, making order in the system structure, decreasing its complexity, and on the other hand, they lead to the cloning of information objects. In the evolution of an open system the increase of information flows and objects complicates the information component that in turn causes an increase of the chaotic processes, which transfer the system into a state of dynamic chaos. Reflecting the above analysis of the interaction of chaotic and stochastic systems, it appears that the dynamic chaos like a random process requires a statistical description. Dynamical systems with complex trajectories can be described in terms of the geometry of limit sets in the phase space, as well as the evolution of the phase trajectories in time. One of the fundamental peculiarities of the temporal dynamics of systems is the so called Poincare reversion. Poincare reversion means that any trajectory, starting from a point will endlessly pass in time as close as possible to the initial state. Such movements in dynamic systems Poincare called the Poisson stability. The examples of such systems are the systems implementing the conditions of the attractor