pacemaker
Class MaSModel

java.lang.Object
  pacemaker.MaSModel

public class MaSModel
extends java.lang.Object

Useful static code related to Phase Response Curve (PRC) related to "MAS" model (Mirollo and Strogatz 1990).

PRC is a function in the x,y-plane (in the square (0,0)-(1,1)) that shows the relation between:

1. the phase (the moment during the period)
2. the amount of eccitation accumulated (eccitation increases during the period, when it reach the threshold, the firefly emits a flash)

(threshold is at value 1,1)

The function will be the classic

f(x)=1/b*log(1+x*(exp(b)-1)) (Mirollo and Strogatz 1990, Fig. 1)

that is a monotonic increasing, concave-down function moving from (0,0) to (1,1).

The parameter named 'b' influences the shape of the PRC in the plane. (see Mirollo and Strogatz 1990, Fig. 3).

b must be in the range ]0,+inf] for the definition of f(x). When b approaches 0, f(x) resembles the identity function (y=x). But when b exactly =0, the function shape degenerates cause of mathematical infinites, although reasonably she should fit exacly the identity. We overcome it in this implementation: when you supply b=0 we will substitute the above f(x) with identity f(x)=x.

Constructor Summary

MaSModel()

Method Summary

static double	eval_inverse_PRC(double y, int b) Evaluate the inverse function f-1 of the PRC: given the y value, you get the x value (the phase).
static double	eval_PRC(double phase, int b) Evaluates the PRC for the given phase (x).
static void	main(java.lang.String[] args) For testing purposes

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

MaSModel

public MaSModel()

Method Detail

eval_PRC

public static double eval_PRC(double phase,
                              int b)

Evaluates the PRC for the given phase (x).

1. f(x)=x if b=0.

2. f(x)=1/b*log(1+x*(exp(b)-1)) if b=0.

Parameters:

phase - - the phase (x value) proportional to period. In range [0,1]. If longer than the actual period, is beyond the f(x) definition. In this case, always 1 is returned (and in implementation, this will probably trigger the execution of a flash immediately)

Returns:

PRC evaluation (y value): in range [0,1].

eval_inverse_PRC

public static double eval_inverse_PRC(double y,
                                      int b)

Evaluate the inverse function f-1 of the PRC: given the y value, you get the x value (the phase).

eval_prc(double, int)

Parameters:

y - - y value, in range [0,1]

Returns:

x value - the phase. In range [0,1].

main

public static void main(java.lang.String[] args)

For testing purposes