The tree of multistable regimes.
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.
The schematic diagram of the controller.
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.
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 .
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.
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.
Phase portrait and cross-spectrum of (a) , (b) , and (c) oscillations. Parameters' values are: .
Projection of the phase portrait (a) and the cross-spectrum (b) of chaotic attractor formed from oscillations under -phase influence at .
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.
The structure of synchronization areas at different values of phases of the external forces from till .
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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