Abstract
In this paper, we present a scheme for uncovering hidden chaotic attractors in nonlinear autonomous systems of fractional order. The stability of equilibria of fractional-order systems is analyzed. The underlying initial value problem is numerically integrated with the predictor-corrector Adams-Bashforth-Moulton algorithm for fractional-order differential equations. Three examples of fractional-order systems are considered: a generalized Lorenz system, the Rabinovich-Fabrikant system and a non-smooth Chua system.
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Notes
Recently, based on philosophical arguments rather than a mathematical point of view, some researchers questioned the appropriateness of using initial conditions of the classical form in the Caputo derivative [41]. However, it should be emphasized that, in practical (physical) problems, physically interpretable initial conditions are necessary and Caputo’s derivative is a fully justified tool [42].
The geometric multiplicity represents the dimension of the eigenspace of the corresponding eigenvalues.
In many cases, one can simplify this procedure and consider instead a path in the space of parameters, such that the starting point of the path corresponds to a self-excited attractor.
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MF Danca is supported by Tehnic B SRL.
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Danca, MF. Hidden chaotic attractors in fractional-order systems. Nonlinear Dyn 89, 577–586 (2017). https://doi.org/10.1007/s11071-017-3472-7
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DOI: https://doi.org/10.1007/s11071-017-3472-7