Applications · Engineering
Chaos in electronic circuits
Chua's 1983 circuit was the first electronic device explicitly engineered to be chaotic. Today chaos is used in secure communication, broadband signal generation, and as a physical entropy source.
Virtual oscilloscope: Chua's circuit
(v_C1, v_C2) phase portrait: double scroll
Chua's circuit
dv_C1/dt = α (v_C2 − v_C1 − f(v_C1))
dv_C2/dt = v_C1 − v_C2 + i_L
di_L/dt = −β v_C2
f(v) = m₁ v + 0.5 (m₀ − m₁) (|v + 1| − |v − 1|) Chua diode
classical: α = 15.6, β = 28, m₀ = −1.143, m₁ = −0.714
The oscilloscope shows aperiodic broadband waveforms;
the phase portrait reveals the double-scroll attractor.Chua's circuit
Two capacitors, one inductor, one nonlinear resistor (Chua diode) realise the double-scroll attractor. Implementable with op-amps in a few minutes, this is the textbook hardware experiment for chaos.
Memristive chaos
Itoh-Chua and Bao circuits replace the Chua diode with a memristor, producing rich families of multi-scroll attractors useful for chaos cryptography.
Chaos shift keying
Encode bits as parameter choices for a chaotic system and transmit the chaotic waveform. The receiver synchronises via Pecora-Carroll and demodulates by matching the waveform. Practical limitations: noise, sync failure, low data rate.
See also
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