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Generic model of pattern formation in nonlinear systems with two spatial scales

Dr. Sergio Alonso:

 

Pattern formation is typically obtained in nonlinear systems from an unstable homogeneous state. The resulting process happens with characteristic spatial and temporal scales. However, two instabilities with different spatial scales can appear simultaneously in multiscale systems. Such type of behaviors can be observed in extended chemical systems and in protein and phospholipid dynamics in biological membranes.
Here, we couple two simple systems, each of them giving rise to pattern formation. The dynamics of the whole system di ffers substantially from the original uncoupled dynamics, and a codimension-two point between wave and Turing instabilities is observed. The coexistence of the di fferent patterns and the corresponding dominance is studied with the amplitude equations obtained from the coupled system. Finally, delay feedback is employed to control the dominant instability.

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