Data, figures and code for: A single oscillator response sets the exponents of synchronization transitions

Abstract

Changes in v1.0.7. Two faults in the cavity figure, both found on the page. The near lower corner of the box at the far end was missing, and with it about a sixth of the front lower edge. The two panels of that figure are each wider and taller than the drawing they hold, which is what lets a long flat cavity and a cone be drawn large in one narrow column, so the two panel rectangles overlap. An axes background is opaque white, and the panel added second was painting over the bottom of the first. Measured on the previous layout, three edges of the box reached only 82, 94 and 80 per cent of their length. Neither panel carries a background now and all twelve edges are drawn in full. The panel title was at the same time touching the top of the box, with no white space at all between them; the figure is a little taller and the titles now clear the drawing below them by 33 and 35 pixels at 300 dpi. Neither fault could be seen by the checks already in place, because one looks for text printed on drawing and the other for ink at the edge of the canvas, and a missing piece of drawing is neither. Two checks are added and run on every build: one projects the twelve edges of the cavity with the transform that drew them and samples the render along each, and one measures the white space under each panel title. Four tests are added, one of which turns the backgrounds back on and confirms that a corner then disappears, so the new check is known to be worth running. No computed result changes and the full test suite of 124 tests passes. Simulation records, figures and a frozen copy of the code for the article "A single oscillator response sets the exponents of synchronization transitions" by T. M. Mahim, M. M. Rahman and A. S. M. Mohsin (BRAC University). The work shows that the exponent with which the order parameter grows above a synchronization threshold is set by one object, the locking kernel W(u): the time averaged projection a single oscillator keeps on the collective field, as a function of its detuning in units of the width of the locked region. Replacing the coupling by that width as the variable along the branch turns the self consistency into an exact parametric solution for any frequency distribution and any kernel. The area under the kernel fixes the threshold and its tail alone fixes the exponent, with beta = 1/(s-1) for a tail |u|^-s with 1 < s < 3 and beta = 1/2 for s >= 3. The archive contains two files. lockkernel_data_and_figures_v1.0.7.zip holds every JSON record the reproduction scripts write, their run logs, and the figures of the article. lockkernel_code_frozen_v1.0.7.zip holds a frozen copy of the Python package lockkernel at v1.0.7, the reproduction scripts, the test suite, the packaging files and the licence. Contents of the data record: 01_parametric (the exact parametric solution against two closed forms), 02_universality_line (the exponent along a one parameter family of kernels, and the amplitude), 03_order_of_transition (the sign of the nonlocal integral that decides the order, with the tricritical point), 04_meanfield_check (the time averaged kernel against the full undamped dynamics, 48 runs), 05_solver_validation (the class resolved solver against three independent exact references), 06_coupling_disorder (the averaged kernel and the published network exponent families), 09_quenched_simulation (the same with the disorder drawn once and held fixed), 10_marginal_and_robustness (the marginal case s = 3 and its logarithmic correction). The living repository is https://github.com/Tanvir-Mahmud-Mahim/locking-kernel-universality (Apache 2.0). Requires Python 3.9 or later with NumPy, SciPy, mpmath and Matplotlib. Install with pip install -e . and run pytest, then run the scripts in scripts/ in order to regenerate every record in this archive.