title: Nonlinear effects on Turing patterns: time oscillations and chaos.
abstract: 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.
authors.affiliation: Departamento de Nanotecnología, Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Querétaro, México.
authors.forename: J L
authors.initials: JL
authors.lastname: Aragón
authors.forename: R A
authors.initials: RA
authors.lastname: Barrio
authors.forename: T E
authors.initials: TE
authors.lastname: Woolley
authors.forename: R E
authors.initials: RE
authors.lastname: Baker
authors.forename: P K
authors.initials: PK
authors.lastname: Maini
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D016014:Linear Models; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D010825:Physics / Q000379:methods