Chaotic mathematical circuitry

René Lozi (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

Following the worldwide tradition of use of Chua's circuits for various purposes, we introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry -the design of electronic circuit- especially in the frame of chaotic attractors. An electronic circuit is composed of individual electronic components, such as capacitors, diodes, inductors, resistors, transistors and connected by conductive wires. Recently, in 2009, three more components discovered by L. O. Chua have been added to the set of devices, namely: memristors, memcapacitors and meminductors. In the same way a mathematical circuit is composed of individual components we design: generators, couplers, samplers, mixers, reducers and cascaders, connected by streams of data. The combination of such mathematical components allows many new applications in chaotic cryptography, genetic algorithms in optimization or in control.

Mots clés: mathematical circuitry; Chua's circuit

Domaines: Systèmes dynamiques [math.DS]; Electronique

René Lozi. Chaotic mathematical circuitry. Andrew Adamatzky, Guanrong Chen. Chaos CNN, Memristors and Beyond, A festschrift for Leon Chua, World scientific, pp.307-323, 2013, 978-981-4434-79-9. ⟨hal-00682309v2⟩