Received 26 September 1991

Revised manuscript received 29 January 1992

Accepted 7 February 1992

Ref: G.
Rowlands and J. C. Sprott, Physica D **58**,
251-259
(1992)

The complete paper is available in PDF format.

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Fig. 1. Phase-space plots of the logistic equation (a) from original
data and (b) after singular value decomposition.

(a)

(b)

Fig. 2. Phase-space plots of the Henon map (a) from original data
and
(b) after singular value decomposition.

(a)

(b)

Fig. 3. Phase-space plots of the Henon map (a) with noise added and
(b) from a solution of the model equations fit to the noisy data. A
comparison
of (b) with fig. 2a shows that the method has completely removed the
noise
and restored the original.

(a)

(b)

Fig. 4. Three-dimensional phase-space plots of the Lorenz attractor
showing that the topology of the attractor is preserved. (a) Original
input
data, (b) result of singular value decomposition, and (c) solution of
the
model equations.

(a)

(b)

(c)

Fig. 5. Three-dimensional phase-space plots of the Rossler attractor
showing that the topology of the attractor is preserved. (a) Original
input
data, (b) result of singular value decomposition, and (c) solution of
the
model equations.

(a)

(b)

(c)

Fig. 6. (a) Variation of the nine largest coefficients of the model
equations with the parameter r in the Lorenz equations, (b) along with
a least squares fit of each coefficient to a cubic polynomial in r.

(a)

(b)

Fig. 7. Phase-space portraits for the Lorenz attractor with r=57 (a) obtained directly from singular value decomposition, and (b) resulting from solution of the model equations with coefficients calculated from least squares fits to cubic polynomials in r.