. Design for a brain. Brain -- Physiology; Central nervous system -- Mathematical models; Neurophysiology. 4/9 DESIGN FOR A BRAIN A is then found to be stable, and the line from B unstable. This example makes it obvious that the concept of ' stability ' belongs primarily to a line of behaviour, not to a whole field. In particular it should be noted that in all cases the definition gives a unique answer once the line, the region, and the initial state are given. The examples above have been selected to test the definition severely. Sometimes the fields are simpler. In the field of the cube, for
. Design for a brain. Brain -- Physiology; Central nervous system -- Mathematical models; Neurophysiology. 4/9 DESIGN FOR A BRAIN A is then found to be stable, and the line from B unstable. This example makes it obvious that the concept of ' stability ' belongs primarily to a line of behaviour, not to a whole field. In particular it should be noted that in all cases the definition gives a unique answer once the line, the region, and the initial state are given. The examples above have been selected to test the definition severely. Sometimes the fields are simpler. In the field of the cube, for instance, it is possible to draw many boundaries, each oval in shape, such that all lines within the boundary are stable. The field of the Watt's governor is also of this type. It will be noticed that before we can discuss stability in a particular case we must always define which region of the phase-space we are referring to. A field within a given region is ' stable ' if every line of behaviour in the region is stable. A system is ' stable ' if its field is stable. 4/9. A resting state is one from which an absolute system does not move when released. Such states occur in Figure 4/3/1 at A and B, and in Figure 4/5/1 at the origin. Although the variables do not change value when at a resting state this invariance does not imply that the ' machine ' itself is inactive. Thus, a steady Watt's governor implies that the engine is working at a non-zero rate. And a living muscle, even if unchanging in tension, is continually active in metabolism. 4 Resting ' applies to the variables, not necessarily to the ' machine ' that yields the variables. 4/10. If a line of behaviour is re-entrant to itself, the system undergoes a recurrent cycle. If the cycle is wholly contained in a given region, and the lines of behaviour lead into the cycle, the cycle is stable. Such a cycle is commonly shown by thermostats which, after correct- ing any gross displacement, settle down to a steady oscillatio
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