The file janus.py is a python script to numerically integrate Janus oscillator networks using SciPy's Complex-valued Variable-coefficient Ordinary Differential Equation solver. The file plot.nb is a Mathematica notebook which can be used to plot results. The folder data contains the output generated by the examples below.
This python code has been run with anaconda2 and anaconda3, either of which can be downloaded from the Anaconda website: https://www.anaconda.com/download/#macos. It requires packages numpy, scipy, and progressbar. Create an environment with these packages with conda create -n janus_env scipy numpy progressbar and activate it with source activate janus_env. The Mathematica code has been run with Mathematica 11.1.1.0.
Running the terminal command ./janus.py -h will give a usage message with command line argument descriptions.
usage: janus.py [-h] --filebase FILEBASE [--sweep {0,1}] [--output {0,1}]
[--number NUMBER] [--time TIME] [--atime ATIME]
[--rtime RTIME] [--dt DT] [--avgcount AVGCOUNT]
[--threshold THRESHOLD] [--beta0 BETA0] [--beta1 BETA1]
[--sigma0 SIGMA0] [--sigma1 SIGMA1] [--delta0 DELTA0]
[--delta1 DELTA1] [--omega1 OMEGA1] [--omega2 OMEGA2]
[--iseed ISEED] [--hseed HSEED] [--dsigma DSIGMA]
[--rthreshold RTHRS] [--pthreshold PTHRS]
[--neighbors NEIGHBORS] [--links NUMLINKS] [--dimension {1,2}]
Numerical integration of networks of Janus oscillators.
optional arguments:
-h, --help show this help message and exit
--filebase FILEBASE Base string for file output
--sweep {0,1} Flag to run a branch sweep; 0 for single runs and 1
for sweeps. Default 0.
--output {0,1} Flag for output style; 0 for abbreviate data and 1 for
full data. Default 0.
--number NUMBER Number of Janus oscillators. Default 50.
--time TIME Total integration time. Detault 10000.
--atime ATIME Time to adiabatically change coupling from sigma0 to
sigma. Default 0.
--rtime RTIME Time to start averaging order parameter. Default 9000.
--dt DT Time between outputs. Default 0.1.
--avgcount AVGCOUNT Number of timesteps to average over for cluster
counting. Default 10.
--threshold THRESHOLD
Frequency difference threshold for cluster counting.
Default 0.01.
--beta0 BETA0 Initial internal coupling constant. Default 0.25.
--beta1 BETA1 Final internal coupling constant. Default 0.25.
--sigma0 SIGMA0 Initial external coupling constant. Default 0.4.
--sigma1 SIGMA1 Final external coupling constant. Default 0.4.
--delta0 DELTA0 Initial frequency heterogeneity. Default 0.0.
--delta1 DELTA1 Final frequency heterogeneity. Default 0.0.
--omega1 OMEGA1 Natural frequency 1. Default 0.5.
--omega2 OMEGA2 Natural frequency 2. Default -0.5.
--iseed ISEED Initial condition random seed. Default 5.
--hseed HSEED Heterogeneity profile random seed. Default 1.
--dsigma DSIGMA Coupling strength sweep step size. Default 0.002.
--rthreshold RTHRS Threshold change in order parameter to stop branch
sweep. Default 0.05.
--pthreshold PTHRS Threshold change in num locked to stop branch sweep.
Default 5.0.
--neighbors NEIGHBORS
Number of neighbors. Default 1.
--links NUMLINKS Number of random small-world links. Default 0.
--dimension {1,2} Network structure dimension. Default 1. --dimension 2
has not been tested for all options.
For backwards-compatibility with previous command line argument structure, running the terminal command python janus.py will produce the different usage message below. Either style of command line arguments will function. In the new style, the --sweep 0 argument corresponds to usage 1 below, and the --sweep 1 argument corresponds to usage 2 below. In the new style, the first example can be run with ./janus.py --filebase data/random/random, and the second can be run with ./janus.py --time 10000 --atime 4000 --rtime 5000 --sweep 1 --filebase data/branches/chimera.
Usage will depend on number of command line argument
usage 1: `python explosive.py [N] [t1] [t2] [t3] [dt] [avgcount] [thrs] [beta0] [beta] [sigma0] [sigma] [delta0] [delta] [seed] [seed2] [filebase] [output]`
Used for single simulation runs with adiabatic parameter changes
N is the number of oscillators
t1 is the total integration time
t2 is the time to adiabatically change coupling from sigma0 to sigma
t3 is the time to start averaging r
dt is the time between outputs
avgcount is the number of timesteps to average over for cluster counting
thrs is the frequency difference threshold for cluster counting
beta0 is the initial internal coupling constant
beta is the final internal coupling constant
sigma0 is the initial external coupling constant
sigma is the final external coupling constant
delta0 is initial frequency heterogeneity
delta is final frequency heterogeneity
seed is random seed for initial condition (if filebaseic.dat does not exist, otherwise initial conditions from file are used)
seed2 is random seed for heterogeneity
filebase is the output file string base; output files are filebaseout.dat and filebaseorder.dat
output is 1 to output time data and 0 for shorter output
Example 1) `python janus.py 50 10000 0 9000 0.1 10 1e-2 0.25 0.25 0.4 0.4 0.0 0.0 5 1 data/random/random 1`
This example will likely produce a chimera state. The final state data/random/randomfs.dat can be copied to chimeraic.dat to save as an initial condition. Run the following command to copy the file for Example 2 below.
`mkdir -p data/branches && cp data/random/randomfs.dat data/branches/chimeraic.dat`
usage 2: `python explosive.py [N] [t1] [t2] [t3] [dt] [avgcount] [thrs] [sigma0] [beta] [delta] [dsigma] [rthrs] [pthrs] [seed2] [filebase]`
Used to adiabatically sweep out a solution branch
N is the number of oscillators
t1 is the total integration time
t2 is the time to adiabatically change coupling from sigma0 to sigma
t3 is the time to start averaging r
dt is the time between outputs
avgcount is the number of timesteps to average over for cluster counting
thrs is the frequency difference threshold for cluster counting
sigma0 is the initial external coupling constant
beta is the internal coupling constant
delta is frequency heterogeneity
dsigma is the coupling strength step
rthrs is the threshold change in order parameter to stop branch sweep
pthrs is the threshold change in num locked to stop branch sweep
seed2 is random seed for the heterogeneity profile
filebase is the output file string base; output files are filebaseout.dat and filebaseorder.dat
Example 2) `python janus.py 50 10000 4000 5000 0.1 10 1e-2 0.4 0.25 0.0 0.002 0.05 5.0 1 data/branches/chimera`
This will sweep out the coupling constant for the chimera initial condition.
Usage 1
The program always appends a summary line of statistics about the simulation to the file filebaseorder.dat, which contains the coupling constant sigma, the heterogeneity strength delta, the mean order parameter r, and the mean number of phase-locked oscillators Nlocked, where the means are calculated from time t2, to t1, separated by spaces. The program also always saves the final state of the system to filebasefs.dat (which can be copied to another filebaseic.dat to use as initial conditions elsewhere). If the output flag is set to 1, the program also creates a file filebaseout.dat that contains more detailed data. The first line of filebaseout.dat contains the command line that ran the program. The second line contains the natural frequencies of each phase oscillator in each Janus oscillator. The third line contains the instantaneous order parameter at each timestep. The next 2N lines contains the phases of each phase oscillator in each Janus oscillator for each timestep. The next N lines contains the adjacency matrix of the network of phase oscillators. If the output flag is high, the program also creates a file filebaseclusters.dat that contains information about which oscillators were deemed instantaneously phase-locked. Each line corresponds to every avgcount timesteps. The first N entries of each line are 0 for unlocked oscillators and 1 for locked oscillators. The remaining entries on these lines are the average instantaneous phase velocity for each of the oscillators that was deemed locked.
Usage 2
The program creates a filebasesweep.dat, which contains the summaries in the form of the filebaseorder.dat from usage 1 for each sigma in the branch sweep. The program also creates a filebasecrits.dat which contains the smallest and largest values of the coupling constant sigma for which the branch exists.