Complex Neuro-Cognitive Systems - Foundations on Natural and Artificial Computation - page 7

Fig. 2. Reductionist, deductive explanation is illustrated by following the path through
cells A → B → C → D . This approach fails in non-decomposable systems with complex
dynamics since no system equations can be established. Instead, observable behaviour
of the real system is explained by nonlinear dynamic analysis, i.e. move C → D is to
be made (inspired by [16]).

neuroscience. Let us consider the situation presented in Fig. 2. In cell A the
physical system under study is displayed (a human's head with EEG recording
sites). Cell B shows a formal model (a system of nonlinear differential equations).
Establishing the model requires that all the variables determining the system and
their dynamic connections are exactly known. In cell C the phase portrait in the
system state space is schematically illustrated. It allows to describe the possible
system behaviour in terms of trajectories, attractors, bifurcations etc. Cell D
presents the observed system behaviour which is often measured in cognitive
science in the form of time series (in this case the EEG activity recorded via
several channels).
The usual kind of reductionist, deductive explanation can be illustrated by
following the path through cells A D in Fig. 2. The behaviour of

the physical system as measured at the emergent level is reduced via the formal
model to the lower level of the physical substrate. The transitions between the
fields are all non-trivial. Move A

→ B → C →

B requires to determine the relevant system
variables and to study their dynamics which is rather unfeasible in the case
of neuro-cognitive systems. Move B

→

C means nonlinear dynamical analysis
of system equations which may pose serious diculties, depending on system

→