Quantification of time scale separation using sojourn time in nullclines #50
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ftavella
reviewed
Mar 19, 2024
| period = 1 / mean(calculate_main_frequency(ode_solution, length(ode_solution.t), length(ode_solution.t))["frequency"]) | ||
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| idx_last_cycle = ode_solution.t .> ode_solution.t[end] - period |
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Why is this necessary? We should add a comment here explaining why
| # add one more data point to fully complete a cycle | ||
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| function gradient(v, grid) |
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Is this function defined inside calculate_sojourn_time_fractions_in_nullclines because it uses information that is only within the scope of that function? If not it should be defined outside as its own separate function for clarity
| @test max_sojourn_time[4] > max_sojourn_time[8] | ||
| @test max_sojourn_time[4] > max_sojourn_time[9] | ||
| @test max_sojourn_time[4] > max_sojourn_time[10] |
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We could also add a test comparing 3 and 4 just in case
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Regarding issue #45, this PR implements a function
calculate_sojourn_time_fractions_in_nullclineswhich calculates the time fraction that an oscillation stays near the nullcline of each variable. It returns a numerical vector of which length equals the dimension of the problem and each element is between 0 and 1 by design. Its element close to 1 implies that the dynamics occurs near the nullcline of the corresponding variable, which lets us to identify a slowly-varying variable. Thus this function can be used to quantify the concept of the time scale separation in relaxation oscillators. For example,maximum(calculate_sojourn_time_fractions_in_nullclines(ode_solution))close to 1 can be interpreted as the dynamics being relaxation oscillator-like having sharp transitions between slow states.