We study systems in which the structure of the circuit or system depends on the dynamical response. In the present paper, observations of behaviours in complex systems where abrupt changes in the character of the motion (or of the time series) are observed, are presented. The possibility of sudden changes of behaviour is probably universal in VSSs, and we examine various other systems each of which which may be classified as a VSS.
Sudden changes are sometimes termed intermittencies, and there is a classic report of a type of intermittency, resulting in the interleaving of laminar flow with bursts of chaos, in the papers of Pomeau and Manneville [6][7]. Here we have borrowed the term ``intermittency" to describe other kinds of sudden change in the time series; in the case of the electronic example, there are bursts of extended chaos interspersed with periods of less extended chaos; and in the traffic simulations, there are sudden changes in the mean lifetime of packets on the net.
The bursty trapping is interpreted as evolution in the system dynamics, in the sense that, as time progresses, the dynamics change discontinuously. Since in a VSS, the system dynamics control the structure of the system, it follows that in a system which traps, the system can be engineered to evolve. This paper makes the suggestion that artificially contrived VSSs may be used as test-beds for studies of the time-development of complex systems.
A common reaction on being presented with an abrupt change of behaviour is to seek out the immediate cause. Often this is done with a view to removing the immediate cause and thus to smooth out the behaviour, or to ``control the chaos", in order to make it more predictable and tractable. In many cases control of irregular behaviour is not possible; the attempts to control the chaos by contingent changes in parameters merely serve to turn the system into a VSS which can then display even more irregular behaviour.
The experiments we have made on the disparate systems, electronic experiments and network simulations, and the impacting oscillator study, all give a view of such behaviour; that the irregularities grow naturally out of the dynamics, which can occur in a closed autonomous system and not be consequences of externally time-varying parameters.