ON TURING-HOPF INSTABILITIESIN REACTION-DIFFUSION SYSTEMS

摘要

We examine the appearance of Turing instabilities of spatially homogeneous periodicsolutions in reaction-diffusion equations when such periodic solutions are consequenceof Hopf bifurcations. First, we asymptotically develop limit cycle solutions associatedto the appearance of Hopf bifurcations in reaction systems. Particularly, we will showconditions to the appearance of multiple limit cycles after Hopf bifurcation. Then, wepropose expansions to normal modes associated with Turing instabilities from spatiallyhomogeneous periodic solutions associated to limit cycles which appear as a consequenceof a Hopf bifurcation. Finally, we discuss examples of reaction-diffusion systems arisingin biology and chemistry in which can be observed spatial and time-periodic patterning.