Turing's diffusion-driven instability for the standard two species reaction-diffusion system is only achievable under well-known and rather restrictive conditions on both the diffusion rates and the kinetic parameters, which necessitates the pairing of a self-activator with a self-inhibitor. In this study we generalize the standard two-species model by considering the case where the reactants c...

Stationary and oscillatory localized patterns (oscillons) are found in the Belousov-Zhabotinsky reaction dispersed in Aerosol OT water-in-oil microemulsion. The experimental findings are analyzed in terms of subcritical Hopf instability, subcritical Turing instability, and their combination.

We study pattern formation arising from the interaction of the stationary Turing and wave ~oscillatory Turing! instabilities. Interaction and competition between these symmetry-breaking modes lead to the emergence of a large variety of spatiotemporal patterns, including modulated Turing structures, modulated standing waves, and combinations of Turing structures and spiral waves. Spatial resonan...

We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive active ternary mixtures, respectively. Already linear stability analysis of the homogeneous mixed state shows that activity not only allows usual large-scale stationary (Cahn-Hilliard) instability well known case but also small-scale (Turing) oscillatory (Hopf...

Abstract The reaction–diffusion models can reproduce a wide variety of exquisite spatio-temporal patterns arising in embryogenesis, development and population dynamics due to the diffusion-driven (Turing) instability [102, 162].

A new type of out-of-phase oscillatory Turing pattern is found in simulations of a simple two-variable model of a bistable reaction-diffusion system consisting of an autocatalytic activator reacting with a substrate that is replenished by a flow. This class of models can describe pH oscillators or enzymatic reactions. No Hopf instability is necessary for this type of oscillatory Turing pattern.

Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to case two domains separated by a permeable membrane. To this aim, we study reaction–diffusion system with zero-flux boundary conditions external Kedem-Katchalsky inner use same approach as in classical analysis but applie...