194
A. Jimenez-Rodriguez et al.
Simple Reservoir. The simplest model is a constant rate of decay of e.g., energy,
that can be used to represent deficits such as of water or food [7]. Accordingly,
the physiological state evolves by ˙
x(t) = −αT + u(t), where α is the decay rate,
T represents some internal autonomic response such as heat generation, and
u(t) represents environmental input, e.g., ambient temperature (note that here
f ≡ 0, g(u) = u and h(T ) = αT ).
Thermoregulation. Consider a recent model of thermoregulatory behaviour proposed by [6], according to which agents are exposed to an ambient temperature
x a and exchange heat upon contact with other agents, x c (t), resulting in a body
temperature, x(t), that evolves according to ˙
x(t) = −[k 1 A + k 2 (1 − A)]x(t) +
[k 1 Ax a (t)+k 2 (1−A)x c (t)]+G(t). Here, k 1 and k 2 are thermal conductivity constants for the exposed area, A, and the non-exposed area of the body, and G(t)
is an autonomic heat generation mechanism that encapsulates different physiological heat sources. Again, the three terms in the right hand side correspond to
those of the general model.
Additionally, we propose that at the interface between body and brain i)
the state vector first has to be compared to some desired state (or set point) to
configure deficits or excesses and respond accordingly. Note that the set point can
be variable (allostatic) ii) the corresponding quantities must be normalized and
expressed in a common currency in order to drive behaviour, and iii) responses
to states representing physiological extremes should be differentially weighted to
avoid fatal consequences (see [13,18]). The output of these three transformations
is what we call a drive, and the component transformations can be expressed as
x d = D(x − x p ),
(2)
where D is a non-linear map defined as D = (U ◦ N ), that is, D(x) = U (N (x)).
The component functions correspond to normalization, N , and urgency, U . Normalization should limit values to the interval [0, 1], and may be linear (compression of the original domain) or non-linear (e.g., a sigmoidal relationship
between physiological state and motivation). Urgency expressions should ensure
that extreme values of the physiological range give rise to higher drives than
those closer to the set points.
Motivational Dynamical System
The motivational state of the agent is modelled as a classical particle undergoing random fluctuations, influenced by the potential V (x). The particle can be
thought of as existing in a one-dimensional domain of the generalized motivational space, P, which we assume here is equivalent to the real line.
We consider distinct motivations to correspond with specific locations of
the phase space P (Fig. 1). The energy landscape provided by the motivational
potential specifies regions of minimal energy that trap the particle for a period
in its evolution, with unstable regions serving as barriers. This energy landscape
is changed dynamically as a function of the motivational factors, i.e., the drives.
A. Jimenez-Rodriguez et al.
Simple Reservoir. The simplest model is a constant rate of decay of e.g., energy,
that can be used to represent deficits such as of water or food [7]. Accordingly,
the physiological state evolves by ˙
x(t) = −αT + u(t), where α is the decay rate,
T represents some internal autonomic response such as heat generation, and
u(t) represents environmental input, e.g., ambient temperature (note that here
f ≡ 0, g(u) = u and h(T ) = αT ).
Thermoregulation. Consider a recent model of thermoregulatory behaviour proposed by [6], according to which agents are exposed to an ambient temperature
x a and exchange heat upon contact with other agents, x c (t), resulting in a body
temperature, x(t), that evolves according to ˙
x(t) = −[k 1 A + k 2 (1 − A)]x(t) +
[k 1 Ax a (t)+k 2 (1−A)x c (t)]+G(t). Here, k 1 and k 2 are thermal conductivity constants for the exposed area, A, and the non-exposed area of the body, and G(t)
is an autonomic heat generation mechanism that encapsulates different physiological heat sources. Again, the three terms in the right hand side correspond to
those of the general model.
Additionally, we propose that at the interface between body and brain i)
the state vector first has to be compared to some desired state (or set point) to
configure deficits or excesses and respond accordingly. Note that the set point can
be variable (allostatic) ii) the corresponding quantities must be normalized and
expressed in a common currency in order to drive behaviour, and iii) responses
to states representing physiological extremes should be differentially weighted to
avoid fatal consequences (see [13,18]). The output of these three transformations
is what we call a drive, and the component transformations can be expressed as
x d = D(x − x p ),
(2)
where D is a non-linear map defined as D = (U ◦ N ), that is, D(x) = U (N (x)).
The component functions correspond to normalization, N , and urgency, U . Normalization should limit values to the interval [0, 1], and may be linear (compression of the original domain) or non-linear (e.g., a sigmoidal relationship
between physiological state and motivation). Urgency expressions should ensure
that extreme values of the physiological range give rise to higher drives than
those closer to the set points.
Motivational Dynamical System
The motivational state of the agent is modelled as a classical particle undergoing random fluctuations, influenced by the potential V (x). The particle can be
thought of as existing in a one-dimensional domain of the generalized motivational space, P, which we assume here is equivalent to the real line.
We consider distinct motivations to correspond with specific locations of
the phase space P (Fig. 1). The energy landscape provided by the motivational
potential specifies regions of minimal energy that trap the particle for a period
in its evolution, with unstable regions serving as barriers. This energy landscape
is changed dynamically as a function of the motivational factors, i.e., the drives.