Archive image from page 40 of Design for a brain; the. Design for a brain; the origin of adaptive behavior . designforbrainor00ashb Year: 1960 2/16 DYNAMIC SYSTEMS y = 2-1. On line 2 the state x = 0, y = 2-0 occurred again; but after 0-1 seconds the state became x = 0-1, / = 1-8 and not x = 0-2, y = 2-1. As the two states that follow the state x = 0, y = 2-0 are not equal, the system is not state-determined. A well-known example of a state-determined system is given by the simple pendulum swinging in a vertical plane. It is known that the two variables—(x) angle of deviation of the string fro
Archive image from page 40 of Design for a brain; the. Design for a brain; the origin of adaptive behavior . designforbrainor00ashb Year: 1960 2/16 DYNAMIC SYSTEMS y = 2-1. On line 2 the state x = 0, y = 2-0 occurred again; but after 0-1 seconds the state became x = 0-1, / = 1-8 and not x = 0-2, y = 2-1. As the two states that follow the state x = 0, y = 2-0 are not equal, the system is not state-determined. A well-known example of a state-determined system is given by the simple pendulum swinging in a vertical plane. It is known that the two variables—(x) angle of deviation of the string from vertical, (y) angular velocity (or momentum) of the bob—are such that, all else being kept constant, their two values at a given instant are sufficient to determine the subsequent changes of the two variables (Figure 2/15/1). The field of a state-determined system has a characteristic property: through no point does more than one line of behaviour run. This fact may be contrasted with that of a system that is not state-determined. Figure 2/15/2 shows such a field (the system is described in S. 19/13). The system's regularity would be established if we found that the system, started at A, always went to A', and, started at B, always went to B'. But such a system is not state-determined; for to say that the representative point is leaving C is insufficient to define its future line of behaviour, which may go to A' or B'. Even if the lines from A and B always ran to A' and B', the regularity in no way restricts what would happen if the system were started at C: it might go to D. If the system were state-determined, the lines CA', CB\ and CD would coincide. Figure 2/15/2 : The field of the system shown in Figure 19/13/1. 2/16. We can now return to the question of what we mean when we say that a system's variables have a ' natural' association. What we need is not a verbal explanation but a definition, which must have these properties: (1) it must be in the form of a test,
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