Hyperchaos in coupled Colpitts oscillators

The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual chaotic signals, v(t) = (v(1) + v(2))/2.

The corresponding differential equations have been derived. The results of both, numerical simulations and hardware experiments are presented. The coupling coefficient k proportional to 1/R-k should be small to avoid mutual synchronisation of the individual oscillators. The spectrum of the Lyapunov exponents (LE) have been calculated versus the coefficient k.

For weakly coupled oscillators there are two positive LE indicating hyperchaotic behaviour of the overall system.