Construction of the mathematical example of attractor of Plykin type: The initial domain on the plane (left) and the result of its transformation under a single application of the map (right).
The unit sphere used in the construction of the basic equations.
Stroboscopic portraits of the attractor in three projections obtained from the numerical integration of equations (2). Parameters are assigned according (3).
(Color online) Circuit diagram of the device. Dynamic variables that characterize the position and the phase space on the unit sphere are voltages on the capacitors C1, C2, and C3, respectively, for z, y, x. Multipliers A1, A2, A3, and A7 have positive conversion coefficients for transformation from input to output voltages, and those for A4, A5, and A6 are negative; the absolute value of the conversion coefficients is 0.1.
Time dependences for three variables x, y, z obtained by simulation in MULTISIM with a use of the multi-channel oscilloscope tool.
Spectra of signals corresponding to the variables x, y, z. The resolution frequency is 4 Hz.
Portraits of the attractor in three projections on the planes (x, y), (x, z), and (z, y), obtained from the simulation in MULTISIM by snapshot of the oscilloscope screen.
Portraits of the attractor in the stroboscopic section in projection on the planes (x, y), (x, z), and (z, y), obtained from processing the data of the MULTISIM simulation saved as time series for x, y, z with sample time step 2 ms.
Stroboscopic portraits of attractor depicted on the plane of the variables (3), one obtained from computer integration of equations (2) (a) and the other from processing recorded data of simulation of the circuit in MULTISIM (b).
(Color online) Visualization of the contracting and expanding foliations (a) and Markov partition of the absorbing domain containing the attractor (b) obtained numerically from the two-dimensional version of equations (2) reduced to the surface of the unit sphere. Markov partition for the Plykin attractor construction corresponding to Fig. 1 (c), and graph illustrating allowed transitions for the both Markov partitions (d).
Histogram for the distribution of angles α between the subspaces of perturbation vectors corresponding to integration in forward and inverse time along representative orbit on the attractor of the system (2) as explained in the text.
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