When the TOTAL V—total voltage, or in our case the brightness of the combined
flashes—exceeds a given level, each cell boosts its own voltage by a small amount
(BOOST STRENGTH). That boost voltage hastens the time for the receiver to
reach its peak and discharge. Assuming the parameters are within certain limits, this
process generates an outcome where cells gradually merge into synchronous firing.
Even if the cells are significantly different, they can still be driven into synchrony but the reactions times of the cells (DT) must be shorter, the booster signal
strength must be larger, and the resulting synchronous frequency is greater. These
requirements probably mean that the organisms must be more highly developed and
more energy demanding if they are not identical and therefore, the organic forms of
these cells would tend to become genetically more similar through time, at least
with regard to their flashing mechanisms. Such an evolutionary direction would
tend to reduce or even avoid the biological cost of faster reaction times and high
strength booster signals.
In this model we represent four such systems subjected to a common steady
INPUT CURRENT. Reactance (R) is the value of the resistance constant and
Capacitance (C) is the measure of the capacitor constant (Fig. 29.1).
The governing differential equation for each firefly is a simple linear one:
C
à dV=dt þ V=R ¼ INPUT CURRENT ¼ 0:15
ð29:1Þ
that is solved for each of the four such cells.
As shown in Figs. 29.2 and 29.3, the individual and TOTAL V is erratic at first
but grows in size and fluctuation as the cells become synchronized.
Experiment with this model. See what the first DT and BOOST STRENGTH
settings give when the cells are not the same. Change the input current level. All
sorts of interesting results can occur. You should even find, as Strogatz and Stewart
[1] report, that there are a variety of steady conditions where the peaks are not
synchronous. All sorts of interesting possibilities lurk in the dynamics of these two
interconnected pulsing cells.
Think of those thousands of fireflies. Are each of them interconnected to only
one other? Or does each connect to only its nearest neighbors, in a kind of regional
association, with the regions eventually acting as a single unit that must swing
somehow into synchrony with other regional units—a kind of hierarchy of synchronous behavior? Or does each somehow average the peak of the signal from the
whole and adjust its own flash initiation? Add more cells and try out these and
perhaps other ideas. You will find no doubt that this glorious process of nature is not
as complex a process as you might have thought.
We may imagine that the group flashing is the behavior of individuals whose
reproductive chances are enhanced by synchronous behavior—to attract distant
mates into the proximity from a long distance. But what happens when the attracted
mate is close? The appeal of belonging to a group is lost—the act of mating is not a
many-to-one relationship, it is the ultimate in one-to-one behavior. Maybe those in
the vicinity of attractee stop flashing once they realize the situation. Maybe, once
those locals notice the newcomer of the opposite sex, only these locals begin to
242
29 Biosynchronicity
flashes—exceeds a given level, each cell boosts its own voltage by a small amount
(BOOST STRENGTH). That boost voltage hastens the time for the receiver to
reach its peak and discharge. Assuming the parameters are within certain limits, this
process generates an outcome where cells gradually merge into synchronous firing.
Even if the cells are significantly different, they can still be driven into synchrony but the reactions times of the cells (DT) must be shorter, the booster signal
strength must be larger, and the resulting synchronous frequency is greater. These
requirements probably mean that the organisms must be more highly developed and
more energy demanding if they are not identical and therefore, the organic forms of
these cells would tend to become genetically more similar through time, at least
with regard to their flashing mechanisms. Such an evolutionary direction would
tend to reduce or even avoid the biological cost of faster reaction times and high
strength booster signals.
In this model we represent four such systems subjected to a common steady
INPUT CURRENT. Reactance (R) is the value of the resistance constant and
Capacitance (C) is the measure of the capacitor constant (Fig. 29.1).
The governing differential equation for each firefly is a simple linear one:
C
à dV=dt þ V=R ¼ INPUT CURRENT ¼ 0:15
ð29:1Þ
that is solved for each of the four such cells.
As shown in Figs. 29.2 and 29.3, the individual and TOTAL V is erratic at first
but grows in size and fluctuation as the cells become synchronized.
Experiment with this model. See what the first DT and BOOST STRENGTH
settings give when the cells are not the same. Change the input current level. All
sorts of interesting results can occur. You should even find, as Strogatz and Stewart
[1] report, that there are a variety of steady conditions where the peaks are not
synchronous. All sorts of interesting possibilities lurk in the dynamics of these two
interconnected pulsing cells.
Think of those thousands of fireflies. Are each of them interconnected to only
one other? Or does each connect to only its nearest neighbors, in a kind of regional
association, with the regions eventually acting as a single unit that must swing
somehow into synchrony with other regional units—a kind of hierarchy of synchronous behavior? Or does each somehow average the peak of the signal from the
whole and adjust its own flash initiation? Add more cells and try out these and
perhaps other ideas. You will find no doubt that this glorious process of nature is not
as complex a process as you might have thought.
We may imagine that the group flashing is the behavior of individuals whose
reproductive chances are enhanced by synchronous behavior—to attract distant
mates into the proximity from a long distance. But what happens when the attracted
mate is close? The appeal of belonging to a group is lost—the act of mating is not a
many-to-one relationship, it is the ultimate in one-to-one behavior. Maybe those in
the vicinity of attractee stop flashing once they realize the situation. Maybe, once
those locals notice the newcomer of the opposite sex, only these locals begin to
242
29 Biosynchronicity