Abstract
In this paper, we present families of piecewise linear systems which are controlled by a continuous piecewise monoparametric control function for the generation of monoparametric families of multi-scroll attractors. Thus, the maximum range of values that the parameter set can take in order to preserve the useful dynamics for generating of multi-scroll attractors is found and it will be called maximal robust dynamics interval. This class of dynamical systems is the result of combining two or more unstable “one-spiral” trajectories. We give necessary and sufficient conditions in order to preserve multi-scroll attractors in terms of a parameter, i.e., a family of multi-scroll attractors is generated by means of a family of switching systems with multiple monoparametric companion matrices. Lastly, we provide an example to show how the developed theory works.
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Acknowledgments
The first author wants to thank CONACYT for its PhD scholarship support. E.C.C. acknowledges the CONACYT financial support through Project No. 181002. López-Renteria wants to thank CONACYT by the postdoctoral grant number 290941-UIA.
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Communicated by Paul Newton.
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Díaz-González, E.C., López-Rentería, JA., Campos-Cantón, E. et al. Maximal Unstable Dissipative Interval to Preserve Multi-scroll Attractors via Multi-saturated Functions. J Nonlinear Sci 26, 1833–1850 (2016). https://doi.org/10.1007/s00332-016-9321-x
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DOI: https://doi.org/10.1007/s00332-016-9321-x