Name
Abstract | ||
|---|---|---|
Turing–Hopf instabilities for reaction-diffusion systems provide spatially inhomogeneous time-periodic patterns of chemical
concentrations. In this paper we suggest a way for deriving asymptotic expansions to the limit cycle solutions due to a Hopf
bifurcation in two-dimensional reaction systems and we use them to build convenient normal modes for the analysis of Turing
instabilities of the limit cycle. They extend the Fourier modes for the steady state in the classical Turing approach, as
they include time-periodic fluctuations induced by the limit cycle. Diffusive instabilities can be properly considered because
of the non-catastrophic loss of stability that the steady state shows while the limit cycle appears. Moreover, we shall see
that instabilities may appear even though the diffusion coefficients are equal. The obtained normal modes suggest that there
are two possible ways, one weak and the other strong, in which the limit cycle generates oscillatory Turing instabilities
near a Turing–Hopf bifurcation point. In the first case slight oscillations superpose over a dominant steady inhomogeneous
pattern. In the second, the unstable modes show an intermittent switching between complementary spatial patterns, producing
the effect known as twinkling patterns. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s00332-009-9041-6 | J. Nonlinear Science |
Keywords | Field | DocType |
Hopf bifurcation,Turing instabilities,Reaction-diffusion,Averaging,35K57,37G15,34C29 | Oscillation,Bifurcation theory,Limit cycle,Turing,Steady state,Normal mode,Reaction–diffusion system,Classical mechanics,Hopf bifurcation,Mathematics | Journal |
Volume | Issue | ISSN |
19 | 5 | 0938-8974 |
Citations | PageRank | References |
1 | 0.43 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. R. Ricard | 1 | 15 | 2.58 |
| S. Mischler | 2 | 1 | 0.43 |