A simple current-reversible chaotic jerk circuit using inherent tanh(x) of an opamp

A simple current-reversible chaotic jerk circuit is proposed and particularly demonstrates the use of inherently tanh(x) nonlinearity of a single opamp for a chaotic jerk circuit. No additionally nonlinear devices are required. Bifurcation is electronically tunable through a current source in a reversible direction. The largest Lyapunov exponent of either direction forms mirror images, whereas the chaotic attractor of either direction forms anti-symmetric images. Keywords: Chaotic Jerk Oscillator, Current Tunable Classification: Electron devices, circuits and modules [1] K.M. Coumo, and A.V. Oppenheim, “Circuit implementation of synchronized chaos with application to communications,” Phys. Rev. E 71, (1993) pp. 65-68. [2] K. Cho and T. Miyano, “Chaotic Cryptography Using Augmented Lorenz Equations Aided by Quantum Key Distribution,” IEEE Trans. Circuits and Systems I: Regupar Papers, 62, (2014), pp. 478-487. 
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