Complex Rhythms - The Physics of Birdsong - page 144

function of the variables in the problem. Assuming that within these nuclei
the neurons are densely interconnected on a local scale, we can describe the
activity of the nuclei in terms of averaged quantities i 1 , i 2

satisfying (9.14)

[Schuster et al. 1990].
The arguments of the sigmoidal functions represent the following obser-
vation: inspiration and excitation, if coupled, should inhibit each other. RAm
receives input from RVL (which we model with an average periodic activity,
induced by RA neurons in the case of oscines, and maybe by neurons sen-
sitive to the male song in the brain of female horneros). The function f ( x )
acts as an inhibitor of inspiration, and mimics the action of stretch recep-
tors or CO 2 receptors in the respiratory system [Keener and Sneyd 1998].
The details of these mechanisms are yet to be discovered, but evidence of
somatosensory modulation of ongoing song patterns has been recently pre-
sented [Suthers et al. 2002]
As we have discussed, different forcing frequencies can lead to different
respiratory patterns. We assume that 1 −x can represent the air sac pressure
(negative x represents small air sacs, and therefore a pressure higher than
atmospheric pressure). In Fig. 9.7, we show numerically generated pressure
patterns. The three segments correspond to the same neural substrate, but
forced with different frequencies (by RA, if we are dealing with oscines). This
is a possible mechanism for the generation of diverse temporal sequences.
For the moment, this mechanism is no more than a speculative, qualitative
one, compatible with the anatomy described so far. However, it highlights the
amount of possible dynamics that can emerge from the interaction between
the body and the nervous system.
The complexity of respiratory patterns that emerges out of the interac-
tion between neural instructions and the body is a nice example of a rich
physiological rhythm. In the literature, several examples have been reported
of this kind of dynamical behavior [Glass 2001], and in many cases, expla-
nations have been sought in the richness of solutions of nonlinear systems.
What remains rather poorly understood is whether complex dynamics are an
essential feature, or a consequence of the processes of the interaction with en-
vironment. A mechanism such as the one described in this section highlights
the enormous richness of possibilities that a nonlinear substrate provides.

9.5 Body and Brain

Much of the study of the behavior that enhances the survival and reproduc-
tion of animals is carried out in terms of its neural control. The emergence of
behavior, however, involves a strong interaction betwen the nervous system,
the morphology and the environment [Chiel and Beer 1997]. From this point
of view, the biomechanics of the peripheral system is a source of opportunities
as well as a source of constraints.