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Using invariants to change detection in dynamical system with chaos. (English) Zbl 1141.37332

Summary: Change detection is the crucial subject in dynamical systems. There are suitable methods for detecting changes for linear systems and some methods for nonlinear systems, but there is a lack of methods concerning chaotic systems. This paper presents change detection techniques for dynamical systems with chaos. We consider the dynamical system described by the time series which originated from ordinary differential equation and real-world phenomena. We assume that the change parameters are unknown and the change could be either slight or drastic. The process of change detection is based on characteristic dynamical system invariants. Changes in the invariants’ values of the dynamical systems are the indicators of change. We propose a method of change detection based on the fractal dimension and recurrence plot. The automatic detection is provided by control charts. Methods were checked by using small data sets and stream data.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37M10 Time series analysis of dynamical systems
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
93C05 Linear systems in control theory
93C10 Nonlinear systems in control theory

Software:

qcc; Fracdim; VRA; Massdal; TISEAN
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References:

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