Towards a second cybernetics model for cognitive systems

We introduce an adaptive system for dynamics recognition. Thereby, an externally presented dynamics (stimulus) is mapped onto a mirror dynamics which is capable to simulate (simulus). A sudden change of the external dynamics leads to an surprisingly quick re-adaptation of the simulus, even if the presented dynamics is chaotic. The system consists of an internal pool of dynamical modules. The modules are forced to the latter dynamics in the sense of Pyragas' control mechanism by the stimulus. The control term, i.e. the strength of forcing, is used as a measure for which modules fit best to the external dynamics. In a sense, this defines a “dynamics-gradient” within the pool. The mirror dynamics now can be constructed by a linear combination of the best fitting modules with weights given by the control term amplitudes. If one adds the so-constructed mirror dynamics to the pool, one has a representation of the corresponding external dynamics within the pool. Later if the same external dynamics is presented again an even quicker adaptation is possible since a well-fitting module is already present. In order not to blow up the dimensionality of the pool, one can eliminate modules that have not been used for a long time. In principle, the modules can undergo an internal control. In addition, one principally can introduce evolution within the pool. Therefore, the system is able to show what sometimes is called a “second cybernetics”, i.e. a hyper-dynamics of the dynamics modules.