Equivalence of the continuum limit of the generalized Rِssler system and the chaotic transmission line oscillator

We demonstrate the formal equivalence of the continuum limit of the generalized Rössler system (GRS) with a chaotic transmission line oscillator. To establish the connection between these systems, we first present an electronic circuit implementation of the GRS with finite phase space dimension. The circuit consists of a ladder of discrete inductors and capacitors terminated at one end by a negative resistor and at the other with a nonlinear device. In the continuum limit, we find that the ladder of inductors and capacitors becomes a transmission line. The negative resistance and nonlinear termination produce a chaotic transmission line oscillator. This result connects two lines of inquiry in the literature on delay dynamical systems where hitherto no obvious relation was evident. We exploit this connection to confirm predictions of the divergence of the Lyapunov dimension and metric entropy for the continuum GRS made based on extrapolation from finite dimension cases [Th. Meyer, M.J. Bunner, A. Kittel, J. Parisi, Hyperchaos in the generalized Rössler system, Phys. Rev. E 56 (1997) 5069–5082].