Chaos Lab

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

Back to all applications.

Quick quiz

Test yourself on circuits

8 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.First chaotic circuit purpose-built was:

  2. Q2.Chua diode v-i is:

  3. Q3.Colpitts oscillator can be chaotic when:

  4. Q4.Memristive chaotic circuits (Itoh-Chua, Bao) feature:

  5. Q5.Chaos shift keying transmits bits by:

  6. Q6.Chaos masking (communications) hides a message:

  7. Q7.Practical drawbacks of chaos-based communication:

  8. Q8.Chua's circuit has experimental implementations using:

0 of 8 answered