Interrelated Dynamical Systems with Random Initial Inputs
Date Issued
2009
Date
2009
Author(s)
Nian, Zhi-Zhang
Abstract
We consider deterministic dynamical systems with random initial inputs, where we can know that the only uncertainty in the systems is determined at the beginning. An interesting question arises––how would the system in which the variables are interacted push the correlations between variables into change? In this thesis, we examine the evolution of correlations under difference equations, delayed difference equation (a kind of difference equation) and differential equation separately. As a result, the paths of correlations under different equations have a similar consequence––the patterns of the paths may have a long-term stable tendency or a cycle, simple or complicated, after several periods of evolution. Moreover, this thesis provides a new point of view on dealing with uncertainty and correlations in simulation––the correlations of variables in equations, as time progresses, may not be constant but still predictable. We believe that the thought provides different possible perspectives on other scientific areas, such as statistics and econometrics.
Subjects
dynamical system
random initial values
correlation
differential equation
delay difference equation
Type
thesis
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