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We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems.

Original publication

DOI

10.1103/PhysRevE.86.026201

Type

Journal article

Journal

Phys Rev E Stat Nonlin Soft Matter Phys

Publication Date

08/2012

Volume

86

Keywords

Algorithms, Computer Simulation, Diffusion, Linear Models, Models, Theoretical, Nonlinear Dynamics, Oscillometry, Physics