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Fractal dimension and Wada measure revisited: no straightforward relationships in NDDS

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Abstract

An extended Newton’s discrete dynamical system with a complex control parameter is investigated in this paper. A novel computational algorithm is introduced for the evaluation of Wada measure. A nontrivial relationship between the fractal dimension and the Wada measure is revealed in NDDS. It is demonstrated that the reduction of the fractal dimension of basin boundaries of coexisting attractors does not automatically imply a lower Wada measure of these boundaries. Computational experiments are used to illustrate what impact the complexity of the relationship between fractal dimension and Wada measure does have in practical applications.

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Acknowledgements

Financial support from the Lithuanian Science Council under project no. MIP078 / 15 is acknowledged.

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  1. Department of Mathematical Modeling, Kaunas University of Technology, Kaunas, Lithuania

    Pranas Ziaukas & Minvydas Ragulskis

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  1. Pranas Ziaukas
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  2. Minvydas Ragulskis
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Correspondence to Minvydas Ragulskis.

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Ziaukas, P., Ragulskis, M. Fractal dimension and Wada measure revisited: no straightforward relationships in NDDS. Nonlinear Dyn 88, 871–882 (2017). https://doi.org/10.1007/s11071-016-3281-4

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  • DOI: https://doi.org/10.1007/s11071-016-3281-4

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