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Mixed-mode oscillations in a homogeneous p H-oscillatory chemical reaction system
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10.1063/1.2779857
/content/aip/journal/chaos/18/1/10.1063/1.2779857
http://aip.metastore.ingenta.com/content/aip/journal/chaos/18/1/10.1063/1.2779857
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Experimental reaction cell: (a) reactant inlets, (b) reactor, (c) reactant outlet, (d) magnetic stirrer, (e) pH electrode, (f) inlet and outlet for thermostated fluid.

Image of FIG. 2.
FIG. 2.

Experimental bifurcation diagram: squares, stationary state; full circles, maxima and minima of periodic oscillations within one cycle; empty circles, maxima and minima of aperiodic oscillations. The lines are drawn only for reference.

Image of FIG. 3.
FIG. 3.

Region of hysteresis bounded by a subcritical Hopf bifurcation at and a saddle-node bifurcation on the periodic cycle at . Squares, stationary state; full circles, maxima and minima of periodic oscillations.

Image of FIG. 4.
FIG. 4.

Dynamical regimes as a function of the flow rate : (a) period-1 regime, ; (b) onset of MMOs, ; (c) period-doubled MMOs, ; (d) aperiodic MMOs, ; (e) quasiperiodic-like MMOs, ; (f) quasiperiodic regime, . Note that the pH range is smaller for panels (e) and (f).

Image of FIG. 5.
FIG. 5.

Spectrum of the normalized singular values for the period-doubled mixed-mode regime in Fig. 4(c) .

Image of FIG. 6.
FIG. 6.

Time dependence of the first three modes obtained by SVD (a)–(c) and truncated time series (d) constructed from these modes; corresponding data taken from Fig. 4(c) .

Image of FIG. 7.
FIG. 7.

Attractor reconstructed by SVD for the data from Fig. 4(c) : (a) first three modes in 3D plot; (b) projection onto the plane of the first two modes. The phase point moves counterclockwise.

Image of FIG. 8.
FIG. 8.

Attractor reconstructed by the time-delay method for the data from Fig. 4(c) ; optimal time delay .

Image of FIG. 9.
FIG. 9.

Time plot of the stretching factor for SVD-smoothed data from Fig. 4(c) . The stretching factor does not display any clear linear part, as required for the determination of the maximal Lyapunov exponent. Chosen dimension of embedding is , , (full line); (dashed line); (dotted line).

Image of FIG. 10.
FIG. 10.

Time plot of the stretching factor for the SVD-smoothed data from Fig. 4(d) . The maximal Lyapunov exponent estimated from the linear part (20–170 s) is ; chosen dimension of embedding , , (full line); (dashed line); (dotted line).

Image of FIG. 11.
FIG. 11.

Spectrum of the normalized singular values for the quasiperiodic-like regime in Fig. 4(e) .

Image of FIG. 12.
FIG. 12.

3D plots of the attractor reconstructed from the data in Fig. 4(e) . (a) Reconstruction from the first three modes obtained by SVD; (b) by the time-delay method, optimal time delay .

Image of FIG. 13.
FIG. 13.

Time plot of the stretching factor for SVD-smoothed data from Fig. 4(e) , the Lyapunov exponent estimated from the linear part (20–170 s) is ; chosen dimension of the embedding , , (full line); (dashed line); (dotted line).

Image of FIG. 14.
FIG. 14.

Poincaré section of the attractor shown in Fig. 12(b) , the surface of section taken at pH .

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/content/aip/journal/chaos/18/1/10.1063/1.2779857
2008-03-27
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Mixed-mode oscillations in a homogeneous pH-oscillatory chemical reaction system
http://aip.metastore.ingenta.com/content/aip/journal/chaos/18/1/10.1063/1.2779857
10.1063/1.2779857
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