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Limitations of frequency domain approximation for detecting chaos in fractional order systems. (English) Zbl 1148.65094
Summary: We analytically study the influences of using frequency domain approximation in numerical simulations of fractional order systems. The number and location of equilibria, and also the stability of these points, are compared between the original system and its frequency based approximated counterpart. It is shown that the original system and its approximation are not necessarily equivalent according to the number, location and stability of the fixed points. This problem can cause erroneous results in special cases. For instance, to prove the existence of chaos in fractional order systems, numerical simulations have been largely based on frequency domain approximations, but in this paper we show that this method is not always reliable for detecting chaos. This approximation can numerically demonstrate chaos in the non-chaotic fractional order systems, or eliminate chaotic behavior from a chaotic fractional order system.

MSC:
65P20Numerical chaos
26A33Fractional derivatives and integrals (real functions)
65P40Nonlinear stabilities (numerical analysis)
37D45Strange attractors, chaotic dynamics
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References:
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