Dynamics on membranes mediated
by bulk diffusion

Eliot Fried

Mathematics, Mechanics, and Materials Unit

Okinawa Institute of Science and Technology Graduate University

eliot.fried@oist.jp

    Coupling between an active membrane and bulk diffusion arises in many biological and chemical processes, cell polarization, protein activation waves on cell membranes, cell-to-cell signaling, membrane bound Turing patterns, Belousov-Zhabotinsky reactions on beads, and so on. Although experimental observations demonstrate the presence of collective synchronous and asynchronous behaviors along with other more complicated spatiotemporal pattern dynamics, very little theoretical research has been directed at exploring the processes that govern these phenomena. Assuming Van der Pol oscillator dynamics on the membrane, we identify two essential parameters governing the system. In this two-dimensional parameter space we observe various stable asymptotic dynamics, including synchronous, asynchronous, and decaying behavior. In addition to parameter regions where only one type of asymptotic dynamics occurs, there are also bistable domains. The parameter space contains a degenerate critical point which is considered to be the organizing center of the various dynamical regimes. This is joint work with Johannes Sch`ddot{o}`onke and Toshiyuki Ogawa.

Keyword: pattern formation, collective behavior, bistability