Describing intrinsic noise in Chua's circuit

Exploring an experimental analog Chua’s circuit

“…This direct relation between the Lyapunov diagrams of Figures 3 and 7b, is related to the i D nonlinearity. The cubic function fits better the experimental i D characteristic of the Chua's diode, once that in the experiment the discontinuities of the piecewise linear function become rounded by inaccuracies of the circuit devices and intrinsic noise, as discussed elsewhere [37].…”

“…For A = 10 −6 and A = 10 −5 , we obtain from η(t) = √ 2Ah the noise intensity values 0.14 mV and 0.45 mV, respectively. This means that our noise model adequately mimics the experimental noise and it is a little bit smaller than the noise intensity observed in the real Chua circuit [37].…”

“…Indeed, in general noise tends to distort the parameter planes of any experimental nonlinear system, corroding periodic structures, remaining only chaotic domains as the noise intensity increases [37]. Once that Figure 7b (numerical experiment) is the noiseless case in opposite to Figure 3 (real experiment), we performed a simulation including noise in the model ( 1)-(3) to better compare with results shown in Figure 3.…”

“…To finish this part, we would like to mention that the Gaussian noise distribution, used in this paper and in [37], is well justified. Figure 10 presents the experimental histogram from the fixed point of the inset (a) in Figure 4, which clearly shows a Gaussian behaviour.…”

Universality in spectral condensation

“…The system exhibits period-doubling bifurcation from a fixed point to chaos with change in the resistance, R. Here, we focus on the transition from a fixed point to a period-1 limit cycle. In experiments, external noise or inherent fluctuations including thermal fluctuations of the electronic devices, their inaccuracies and electromagnetic interference will make the fixed point noisy 26 . Thus, for the conditions for which a fixed point is expected, we observe low amplitude noisy oscillations with a broad peak in the power spectrum centered around the natural frequency.…”