Random process representations and some researches of chaos

摘要

In this paper, random process representations of chaotic system and some related researches are proposed. Chaos is generally characterised as a nonlinear, deterministic phenomenon. For a common type of chaotic systems, this paper introduces the equivalent descriptions in the form of random process. Moreover, a problem of the influence on outputs with different random distributions inputs is studied. Such models have many advantages as they much better provide a bridge between chaos and random process. The outputs of this system will be shown to be the random process representation of corresponding chaotic system. Specifically, for the inputs under two given random distributions (normal distribution and uniform distribution), such system will generate exactly the outputs which can obey almost the same distribution as its inputs through the corresponding random process representation of chaos with certain initial condition.