Fig. 1: Chaotic characteristics of the output time traces.

a A schematic of a nanocontact vortex oscillator. b A map of the power spectra as a function of input current amplitudes, \({I}_{{\rm{dc}}}\). The red circles and yellow cross marks indicate a fundamental frequency, \({f}_{0}\), and its upper sideband at \({f}_{0}+{f}_{{\rm{mod}}}\), respectively. \({f}_{{\rm{mod}}}\) is a modulation frequency. c \({f}_{{\rm{mod}}}/{f}_{0}\) as a function of \({I}_{{\rm{dc}}}\). The yellow and red regions represent the commensurate and the incommensurate states, respectively. The dotted horizontal lines indicate plateaus in which the self-phase-locking occurs. d Eighteen different time traces which have identical initial conditions in the commensurate state (\({I}_{{\rm{dc}}}\) = 14.0 mA). e As in d but in the incommensurate state at \({I}_{{\rm{dc}}}\) = 13.2 mA. f Correlation integrals \({C}_{m}(\epsilon )\) as a function of a geometric scaling \(\epsilon\) and g its derivatives of \(\partial {\mathrm{{ln}}}{C}_{m}(\epsilon )/\partial {\mathrm{{ln}}}\epsilon\) for embedding dimensions from \(m=10\) (bottom curve) to \(m=24\) (top curve) by increment of 2. The red and yellow curves are for \({I}_{{\rm{dc}}}\) = 13.2 and 14.0 mA, respectively. The horizontal lines indicated by red and yellow arrows correspond to estimate of \({D}_{{\rm{c}}}\) based on the flats in the scaling \(\epsilon\)-interval \([1,1{0}^{0.3}]\). h Metric \({K}_{2,m}^{\prime}(\epsilon )\) as a function of \(\epsilon\) for embedding dimensions from \(m=10\) (top curve) to \(m=24\) (bottom curve) by increment of 2 at \({I}_{{\rm{dc}}}=13.2\,{\mathrm{{mA}}}\) and i \({\langle {K}_{2,m}^{\prime}(\epsilon )\rangle }_{\epsilon }\) in the scaling range \([1,1{0}^{0.3}]\) for the asymptotic determination of the \({K}_{2}\)-entropy.