One interesting and elusive two-coupled oscillator problem

Chronobiology experiments often reveal intriguing non-linear phenomena, which require mathematical models and computer simulations for their interpretation. One example is shown here, where the two circadian oscillators located in the eyes of the mollusk <i>Bulla gouldiana</i> were isolated and measured <i>in vitro</i>. By maintaining one eye under control conditions and manipulating the period of the second eye, Page and Nalovic (1992) obtained a diversity of results, including synchronized and desynchronized eyes, associated to weak coupling and period differences. A subset of eye pairs, however, showed increasing phase angle followed by phase jumps. These occur and have been satisfactorily modeled in more complex systems where two zeitgebers play clear entraining roles. However, simulations of a simple model of free-running, two mutually coupled limit-cycle oscillators with unilateral change in oscillator period failed completely to reproduce these phase jumps. Here we explain how phase jumps arise in two-zeitgeber systems and then show the closest but unsatisfying, intermediate model that was fit to the <i>Bulla</i> system.