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Controlling phase multistability in coupled period-doubling oscillators
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View: Figures


Image of FIG. 1.
FIG. 1.

The tree of multistable regimes.

Image of FIG. 2.
FIG. 2.

Projection of phase portraits (left and central columns) and cross-spectrum (right columns) of (a), (b), (c), and (d) oscillations; (a) and (b) are plotted at μ = 8.3, while (c) and (d) at μ = 8.48.

Image of FIG. 3.
FIG. 3.

The schematic diagram of the controller.

Image of FIG. 4.
FIG. 4.

The process of directing the trajectory from to oscillations: Time-series of (a), (b), (c), and (d) during the control. Letters A and B mark the largest and the smallest local maxima.

Image of FIG. 5.
FIG. 5.

Dependence of the threshold amplitude value on frequency for transitions (solid line) and (boxes). Letters “a” and “b” are bound the region of the deterministic transition from to .

Image of FIG. 6.
FIG. 6.

Evolution of oscillations under -phase influence at: (a) A = 0.003, (b) A = 0.01, (c) A = 0.011, and (d) A = 0.01. The left column depicts the cross phase portraits, while the middle and the right ones plot the stroboscopic sections and the cross-spectra, respectively.

Image of FIG. 7.
FIG. 7.

The structure of the parameters plane in a vicinity of - subharmonic: is the line of loss of stability of family of regimes, is the line of reverse period-doubling bifurcation of torus, and are boundaries of synchronization tongue for oscillations.

Image of FIG. 8.
FIG. 8.

Phase portrait and cross-spectrum of (a) , (b) , and (c) oscillations. Parameters' values are: .

Image of FIG. 9.
FIG. 9.

Projection of the phase portrait (a) and the cross-spectrum (b) of chaotic attractor formed from oscillations under -phase influence at .

Image of FIG. 10.
FIG. 10.

The power (left column) and the phase (middle column) cross-spectra, and the coherence (right column) of oscillations at different values of the amplitude of the control signals: (a) A = 0, (b) A = 0.003, and (c) A = 0.007.

Image of FIG. 11.
FIG. 11.

The structure of synchronization areas at different values of phases of the external forces from till .

Image of FIG. 12.
FIG. 12.

Synchronization of quasi-periodic oscillations originated from limit cycle under -phase influence at: (a) and (b) A = 0.004, ; (c) and (d) A = 0.007, ; (e) and (f) A = 0.007, .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Controlling phase multistability in coupled period-doubling oscillators