Far East Journal of Dynamical Systems
Volume 14, Issue 1, Pages 35 - 49
(September 2010)
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A CLASS OF DISCRETE DYNAMICAL SYSTEMS DESCRIBED BY PIECEWISE LINEAR FUNCTIONS WITH MULTI-STEP INVARIANT DENSITY
Toshihiko Yasuda
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Abstract:
Nonlinear dynamical systems of simple mathematical models often exhibit extremely complicated behavior, as chaos. In this paper, a class of discrete nonlinear dynamical systems described by some piecewise linear functions with certain multi-step type invariant density are investigated. A method for constructing nonlinear functions with such an invariant density is newly demonstrated. Furthermore, the method for finding the invariant density of the nonlinear functions is also presented. Theoretical analysis is carried out based on the Frobenius-Perron equations. Numerical experiments show the validity of the theoretical analysis, proposed in this paper. |
| Keywords and phrases: chaos, invariant measure, Frobenius-Perron equation, difference equation, piecewise linear function. |
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