**Jesus M. Munoz-Pacheco †, Tonatiuh García-Chávez †, Victor R. Gonzalez-Diaz \*,†, Gisela de La Fuente-Cortes † and Luz del Carmen Gómez-Pavón †**

Faculty of Electronics Sciences, Benemérita Universidad Autónoma de Puebla, Puebla 72000, Mexico; jesusm.pacheco@correo.buap.mx (J.M.M.-P.); tonaspiuck@gmail.com (T.G.-C.);

gise\_tiza@hotmail.com (G.d.L.F.-C.); luz.gomez@correo.buap.mx (L.d.C.G.-P.)

**\*** Correspondence: vicrodolfo.gonzalez@correo.buap.mx; Tel.: +52-222-229-5500

† These authors contributed equally to this work.

Received: 17 February 2020; Accepted: 7 March 2020; Published: 1 April 2020

**Abstract:** This manuscript introduces two new chaotic oscillators based on autonomous Boolean networks (ABN), preserving asymmetrical logic functions. That means that the ABNs require a combination of XOR-XNOR logic functions. We demonstrate analytically that the two ABNs do not have fixed points, and therefore, can evolve to Boolean chaos. Using the Lyapunov exponent's method, we also prove the chaotic behavior, generated by the proposed chaotic oscillators, is insensitive to incommensurate time-delays paths. As a result, they can be implemented using distinct electronic circuits. More specifically, logic-gates–, GAL–, and FPGA–based implementations verify the theoretical findings. An integrated circuit using a CMOS 180nm fabrication technology is also presented to get a compact chaos oscillator with relatively high-frequency. Dynamical behaviors of those implementations are analyzed using time-series, time-lag embedded attractors, frequency spectra, Poincaré maps, and Lyapunov exponents.

**Keywords:** chaotic oscillator; lyapunov exponents; poincare map; integrated circuit; fpga; time-delay; boolean networks
