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Effect of multiple time-delay on vibrational resonance
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10.1063/1.4793542
/content/aip/journal/chaos/23/1/10.1063/1.4793542
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/1/10.1063/1.4793542
View: Figures

## Figures

FIG. 1.

Variation of the response amplitude Q with the parameter g for a few fixed number of time-delayed feedback terms. The values of the parameters are d = 0.5, , f = 0.1, , and . The continuous and dashed lines are the theoretically and numerically calculated values of Q, respectively. In all the subplots, the curve 1 corresponds to . For the curves 2 and 3, the value of γ is 0.3. The values of α for the curves 2 and 3 are 0.5 and 5.5, respectively.

FIG. 2.

Plot of versus γ and α for various values of L. On the plane, in the shaded portions while in the unshaded portions. The curves in the shaded regions show the variation of G with α for a few fixed values of γ.

FIG. 3.

Plot of intervals of α for which as a function of L with . In the remaining intervals of α, we realize .

FIG. 4.

Plot indicating the regions (below the lower curve and above the upper curve for each fixed values of L) in ( ) parameters space where for three fixed values of L and δ. The values of the other parameters are d = 0.5, , f = 0.1, , and .

FIG. 5.

Q 2 (curves 2 and 3) versus g for L = 2, 3, and 6 and for two fixed values of α. The value of δ is 1.9. In all the subplots, Q 1 (curve 1) is also shown to demonstrate the effect of the MTDC on Q 2. The values of α used are: subplot (a): curve 2 (3) , subplot (b): curve 2 (3) , subplot (c): curve 2 (3) . The continuous and dashed curves are theoretically and numerically computed values of Qs, respectively.

FIG. 6.

(a) versus g and (b)–(c) versus g of the two-coupled Duffing oscillators system for L = 2, , and . For details, see the text.

FIG. 7.

(a) and , (b) Q 1 and Q 2, and (c) P 2 versus the control parameter g for L = 2, , and . In the subplot (c), P 2 versus g is shown for also. The two solid circles on the g-axis mark the values of g at which resonance occurs.

FIG. 8.

Phase portraits of co-existing orbits of the second oscillator of the two-coupled Duffing oscillators for a few values of g with L = 2, , and .

FIG. 9.

, difference between the theoretically calculated Qi and the numerically computed Qi , versus i for d = 0.5, , f = 0.1, , L = 2, and for three values of g.

FIG. 10.

Variation of Qi with i for (a) three values of g with L = 2, , and and (b) three values of L with g = 175, , and . The continuous lines and the symbols represent the theoretically and numerically computed values of Qi , respectively.

FIG. 11.

Dependence of on the time-delay α and the number of time-delayed terms L. are alone shown in this plot.

FIG. 12.

Three-dimensional plot of versus δ and α for four fixed values of the number of time-delayed coupling terms. is independent of the parameter g.

FIG. 13.

Qi versus i and g for three values of α with L = 2 and . The thick line represents Q 1.

FIG. 14.

(a) versus δ and α for the system of n-coupled Duffing oscillators with the ITDC. The values of the parameters are d = 0.5, , f = 0.1, . is independent of the parameter g. (b)-(c) Qi versus i and g for two values of α with .

/content/aip/journal/chaos/23/1/10.1063/1.4793542
2013-03-06
2014-04-25

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