Documentation

calculate_amplitude(ode_solution::ODESolution)

Calculate the amplitude of each signal in ode_solution and the relative peak/trough variation.

Arguments

• ode_solution::ODESolution: The full output of the solve() function from DifferentialEquations.jl

Returns

• amplitude_data::Dict: Dictionary containing the amplitude for each signal and the peak/trough variation. The output is encoded as:

amplitude_data = Dict('amplitude' => [amp_signal_1, ..., amp_signal_N], 
                      'peak_variation' => [peak_var_signal_1, ..., peak_var_signal_N], 
                      'trough_variation' => [trough_var_signal_1, ..., trough_var_signal_N])

Notes

• Variation of peaks and troughs is calculated as the standard deviation of all the peaks/troughs in the signal divided by the amplitude. This quantity allows to distinguish stable oscillatory solution from dampened ones.
• To find the most relevant peaks/troughs, we discard any peak/trough that has a prominence less than 1/3 of the total amplitude of the signal (calculated as the maximum - minimum of the signal). Therefore, it is better to use this function with a signal that has little to none transient behavior.

    calculate_main_frequency(ode_solution::ODESolution, sampling::Int, fft_points::Int)

Obtains the dominant frequencies and their powers for each signal on ode_solution via the fast fourier transform

Arguments

• ode_solution::ODESolution: The full output of the solve() function from DifferentialEquations.jl
• sampling::Int: Number of points to be used for uniform re-sampling of ode_solution. The same sampling is used for all signals
• fft_points::Int: Number of points in the frequency spectrum

Returns

• frequency_data::Dict: Dictionary containing the dominant frequencies and their powers for each signal. Here power means the amplitude of that frequency on the FFT spectrum. The output is encoded as:

frequency_data = Dict('frequency' => [freq_signal_1, ..., freq_signal_N], 
                      'power' => [power_signal_1, ..., power_signal_N])

Note

• The provided ode_solution has to be solved with the dense = true setting to be suitable for this function since uniform re-sampling is performed.

is_ODE_oscillatory(frequency_data::Dict, amplitude_data::Dict, freq_variation_threshold=0.05, power_threshold=1e-7, amp_variation_threshold=0.05)

Returns true if an ODESolution is oscillatory based on the calculated frequency and amplitude. False otherwise.

Arguments (Required)

• frequency_data::Dict: The output from calculate_main_frequency
• amplitude_data::Dict: The output from calculate_amplitude

Arguments (Optional)

• freq_variation_threhsold::Real: Maximum tolerated variation in frequency between species in the solution to be declared oscillatory. Default value 0.05.
• power_threshold::Real: Minimum spectral power that the main peak has to have to be declared oscillatory. Default value 1e-7.
• amp_variation_threhsold::Real: Maximum tolerated value for peak/trough variation to be declared oscillatory. Default value 0.05.