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Chaotic systems that are robust to added noise
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View: Figures


Image of FIG. 1.
FIG. 1.

Attractors for Eq. (1) .

Image of FIG. 2.
FIG. 2.

(a) Power spectrum of (peak ). (b) Power spectrum of (peak ).

Image of FIG. 3.
FIG. 3.

Synchronization error as a function of normalized noise rms amplitude for slow time constant (open circles) or 0.01 (filled in squares).

Image of FIG. 4.
FIG. 4.

Sync error as a function of slow time constant . The squares are for , while the triangles are for .

Image of FIG. 5.
FIG. 5.

An unstable periodic orbit for the chaotic system of Eq. (1) .

Image of FIG. 6.
FIG. 6.

(a) and (b) are the nonzero Floquet multipliers for the slow UPO as is changed. The circles are the real parts of the Floquet multipliers, while the triangles are the imaginary parts. There is a bifurcation at .

Image of FIG. 7.
FIG. 7.

Synchronization error as a function of . The rms amplitude of the added Gaussian white noise is twice the rms amplitude of the driving signal. The noise robustness property appears to be lost for , corresponding to the bifurcation in the Floquet spectrum.

Image of FIG. 8.
FIG. 8.

factor for the low-frequency part of the Rossler system as a function of . Note that the vertical axis is logarithmic.

Image of FIG. 9.
FIG. 9.

(a) signal for . Note that there are two frequencies present. (b) signal for . Only one frequency is present.

Image of FIG. 10.
FIG. 10.

Typical slow UPO for the neuron equations, for . (a) shows the fast variables and , while (b) shows the slow variables and .

Image of FIG. 11.
FIG. 11.

UPO seen in the neuron model when (single frequency region), but noise with an amplitude of 0.1 was added. (a) shows the fast variables, and (b) shows the slow variables. Compare this figure to Fig. 10 .


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Scitation: Chaotic systems that are robust to added noise