Practical Problem 13: Pulse Coupled Oscillators

This problem is very similar to the last one. However, here the oscillators are coupled by pulses, short interactions that occur when an oscillators phase reaches a threshold, sends pulses to neighboring oscillators and then experiences a phase reset.

Like in the last problem patches should have two properties phase and dphase. However, the phase variable is defined on the range 0 to 1.

Each oscillator is governed by the equation

$$ \dot\theta = I - \theta $$

where the input $I$ should be a slider variable and have a value $>1$. A good value is $1.2$.

The phases should be initialized (setup) randomly in a range 0 to 1.

independent oscillators

As such the dynamical system above will have each oscillator approach the asymptotic value $I$, so $\theta\rightarrow I$.

However, we will modify the dynamics such that when $\theta$ reaches 1, it will

1. emit a spike
2. be reset to 0

First code the dynamics of independent oscillators

ask patches [
	set dtheta dt * ( I - theta )
	set theta theta + dtheta
	if theta > 1 [
		set theta 0
	]
]

Now write a function that emits a spike to the neighbors with the effect that for those neighbors dtheta will be increased by a positive number $s$. That number should be a slider, also.