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Cross-diffusion in the two-variable Oregonator model
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10.1063/1.4816937
/content/aip/journal/chaos/23/3/10.1063/1.4816937
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/3/10.1063/1.4816937
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Phase diagram in the -ξ plane for ε = 0.04 and  = 0.01, with  =  = 1. BO corresponds to bulk oscillations, (a) to Turing patterns, (b) are quasi-standing waves, (c) is standing waves, (d) is mixture of randomly appearing spots and steady state, (e) is defect-mediated turbulence, and (f) is a mixture of standing waves and defect-mediated turbulence. White zones correspond to a steady state.

Image of FIG. 2.
FIG. 2.

Space-time plots of size 100 space units (horzontal) × 200 time units (downwards), where light (dark) grey levels represents high (low) concentrations of the activator . (a) Turing patterns obtained with  = 0.5 and ξ = −9, (b) quasi-standing waves with  = 2.19 and ξ = −10, (c) standing waves, with  = 2.19 and ξ = −5, (d) randomly appearing spots and steady state with  = 2.25 and ξ = −10.5, (e) defect-mediated turbulence with  = 2.19 and ξ = −1, and (f) mixed pattern with  = 2.19 and ξ = −4. Insets in (e) and (f) show detailed space-time plots of the marked area (50 s. u. × 20 t. u.). Other parameters as in figure 1 . Random initial conditions were used.

Image of FIG. 3.
FIG. 3.

Phase diagram in the -ξ plane for ε = 0.04 and  = 0.05, with  =  = 1. T corresponds to Turing patterns, OT to oscillatory Turing and BO to bulk oscillations. White zones correspond to a steady state.

Image of FIG. 4.
FIG. 4.

(a) Space-time plot of oscillatory Turing patterns with ε = 0.04,  = 0.05,  = 1.7 and ξ = −9.5, with size 100 space units (horzontal) × 200 time units (downwards), where light (dark) color represents high (low) concentration of the activator . (b) Shows a zoom of 50 space units × 25 time units taken from the bottom left of panel (a). Random initial conditions were used.

Image of FIG. 5.
FIG. 5.

Two-dimensional Turing patterns obtained with ε = 0.04,  = 0.01 and  = 0.5, with  =  = 1, (a) labyrinthine pattern obtained with ξ = −9.5, and (b) spot pattern obtained with ξ = −6.5. Snapshots of patterns are taken 150 time units after starting the simulation with random initial conditions. Size of pictures is 50 space units × 50 space units, light (dark) color represents high (low) concentration of the activator .

Image of FIG. 6.
FIG. 6.

Formation of Turing patterns from standing waves, (a) snapshots taken at 1 time unit intervals 11 time units after starting the simulation with random initial conditions, (b) snapshot taken at 248 t. u. after starting the simulation, and (c) space-time plot 50 s. u. (horizontal) × 250 t. u. (downwards) taken at the gray line in the second panel of (a). Size of pictures is 50 space units × 50 space units. Parameters are ε = 0.04,  = 0.01,  = 2.2, ξ = −7, and  =  = 1. Light (dark) color represents high (low) concentration of the activator .

Image of FIG. 7.
FIG. 7.

Space-time plots of size 100 space units (vertical) × 120 time units (downwards) with ε = 0.04  = 0.05,  = 1.4, and  =  = 1. (a) Turing patterns with ζ = 1, (b) spatially modulated bulk oscillations with ζ = 2 (note that jumping waves are generated from a Turing spot in the lower left corner), and (c) jumping waves that are generated at the right boundary with ζ = 3. Light (dark) color represents high (low) concentration of the activator . Random initial conditions were used.

Image of FIG. 8.
FIG. 8.

Phase diagrams in the -ζ plane for ε = 0.04, with  =  = 1. In (a),  = 0.01 and in (b),  = 0.05. T corresponds to Turing patterns, MBO to spatially modulated bulk oscillations, JW are jumping waves, MSA is a mixed state with small amplitude, DT is defect mediated turbulence, and M is a mixed state of Turing patterns and localized standing waves.

Image of FIG. 9.
FIG. 9.

(a) Space time plot of 50 s. u. (horizontal) × 100 t. u. (downwards) taken at the line in the first panel of b. (b) Sequence of snapshots taken at 0.3 t. u. intervals starting 8.7 t. u. after starting the simulation showing the modulated bulk oscillations. (c) Sequence of snapshots taken at 0.2 t. u. intervals starting 90 t. u. after starting the simulation, showing jumping waves. The size of pictures is 50 s. u. × 50 s. u. Parameters are ε = 0.04,  = 0.01,  = 0.55, ζ = 3, and  =  = 1. Random initial conditions were used.

Image of FIG. 10.
FIG. 10.

(a–d) Space-time plots of size 100 space units (vertical) × 100 time units (downwards) with ε = 0.04,  = 0.01,  = 2.19, ξ = −5.5, and  =  = 1. The velocity of the advective field is 0.1 (a), 0.4 (b), 1.6 (c), and 1.7 (d). (e) Phase diagram of patterns obtained. (f) For comparison, phase diagram showing the effect of flow on a systems with wave instability that displays standing waves. SW corresponds to standing waves (as depicted in a), Mixed is a mixed pattern of synchronous standing waves near the inlet and standing waves further down (as depicted in b), SSW corresponds to synchronous standing waves (depicted in c), and C corresponds to a chaotic state (as depicted in d). DSW corresponds to drifting standing waves (g), M corresponds to a mixed pattern of synchronous standing waves and drifting clusters (i), DC corresponds to drifting clusters (j) and S to a stabilized steady state. Synchronous standing waves for the model with waves instability are shown in (h). Figures (f)-(j) are adapted from Ref. .

Image of FIG. 11.
FIG. 11.

Space-time plots for  = 0.01,  = 0.1, and  = 1 with size 100 s. u. (horizontal) × 200 t. u. (downwards), for  = 2.1 (a), 2.16 (b), 2.17 (c), 2.18 (d), 2.19 (e), and 2.2 (f). In (g), the respective phase diagram is shown. C-SW corresponds to states with spatiotemporal chaos and standing waves, BO to bulk oscillations. Random initial conditions were used.

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/content/aip/journal/chaos/23/3/10.1063/1.4816937
2013-07-30
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Cross-diffusion in the two-variable Oregonator model
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/3/10.1063/1.4816937
10.1063/1.4816937
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