Critical behavior for the onset of type-III intermittency observed in an electronic circuit

Abstract

Near the onset of type-III intermittent chaos observed in an autonomous electronic circuit, the critical exponent \ensuremath{\beta} for a relation 〈\ensuremath{\tau}${\mathrm{〉}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\sim}${\mathrm{\ensuremath{\varepsilon}}}^{\mathrm{\ensuremath{\beta}}}$ is experimentally determined, where 〈\ensuremath{\tau}${\mathrm{〉}}^{\mathrm{\ensuremath{-}}1}$ is the inverse of average laminar length and \ensuremath{\varepsilon} is a parameter in the second return map, ${\mathit{I}}_{\mathit{k}+2}$=(1+2\ensuremath{\varepsilon})${\mathit{I}}_{\mathit{k}}$+${\mathit{bI}}_{\mathit{k}}^{3}$. We obtain \ensuremath{\beta}=0.55, which is far from the Schuster theory value (\ensuremath{\beta}=1) and the recent experimental result (\ensuremath{\beta}=0.85) shown by Kahn, Mar, and Westervelt [Phys. Rev. B 45, 8342 (1992)]. Our result is rather close to the theoretical value of 0.5 predicted by Kodama, Sato, and Honda [Phys. Lett. A 157, 354 (1991)]. A similar result is also obtained for the critical behavior of the Lyapunov exponent.