Models can be synthesised first at the level of the circuits involved in the Jacobian matrix (that determines which types and numbers of steady states are consistent with the model), then only at the level of terms of order zero in the ODE's (that determines which of the steady states actually exist), hence the title 'Circular casuality'.
Which steady states are actually present, depends on the values of terms of order zero in the ordinary differential equations (ODEs), and it is easy to find for which values of these terms a given point in phase space is steady. It means that all can be partitioned in the same way as regards the signs of the eigenvalues and thus as regards the precise nature of any steady states that might be present. All these systems have a common Jacobian matrix and for all of them phase space has exactly the same structure. Also, the interest of considering as a model, rather than a well-defined set of differential equations, a variety of systems that differ from each other only by the values of constant terms is emphasised. Some basic rules are recalled, such as the fact that a positive circuit is a necessary condition of multistationarity. As a therapist, it is necessary to determine what type of actions or behaviors from what family members cause the behaviors of the other family members, in other words, how the cycle begins. In particular, a section on circuits, nuclei, and circular causality and a rather detailed description of the analytic use of the generalised asynchronous logical description, together with a brief description of its synthetic use (OreverseO logic). In circular causality, the cause is the result and the result is the cause therefore, this cycle repeats periodically.
#CIRCULAR CAUSALITY SERIES#
The author presents a series of reflections about the methods of formalisation together with the principles that govern the global operation of systems. The problem of disentangling complex dynamic systems is addressed, especially with a view to identifying those variables that take part in the essential qualitative behaviour of systems.
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