Principal bifurcations and symmetries in the emergence of reaction-diffusion-advection patterns on finite domains

Abstract

Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of coexistence and stability of propagating or stationary nonuniform solutions, which for the general case of far from instability onsets, is conducted using spatial dynamics and numerical continuations. The selection is determined by the boundary conditions which either preserve or destroy the translational symmetry of the model. Accordingly, we explain the criterion and the properties of stationary periodic states if the system is bounded and show that propagation of nonlinear waves (including solitary) against the advective flow corresponds to coexisting family that emerges nonlinearly from a distinct oscillatory Hopf instability. Consequently, the resulting pattern selection is qualitatively different from the symmetric finite wavenumber Turing or Hopf instabilities.

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Cited by in corpus (4)

• Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as limiting case of differential advection
• Why Turing mechanism is an obstacle to stationary periodic patterns in bounded reaction-diffusion media with advection
• Drifting solitary waves in a reaction-diffusion medium with differential advection
• Catalytic membrane reactor model as a laboratory for pattern emergence in reaction-diffusion-advection media