Parameter properties of electronic and biological circuits and systems

The question what behaviors can be exhibited by a given electronic circuit upon variation of the parameters, is fundamental to electrical engineering. To efficiently adapt behavior according to need, say from stability to instability, or among stable or unstable periodicities, it is crucial to know how systems (generically and specifically) depend on parameters. Shrimps or swallow-tails are generic, characteristic parameter space regions that yield fixed stable periodic behavior. By dividing the parameter space into stable and unstable dynamical behavior, they provide such guidelines. In applications, shrimps have first been described at great details in the context of laser systems and electronic circuits, but it is still unknown whether they could also be found in realistic models of biophysics (and if so, whether biology exploits this as an alternative computing paradigm). Here, we provide first explicit examples of their existence.