  Classical models of pattern formation are based on diffusion-driven
instability (DDI) of constant stationary solutions of reaction-diffusion
equations, which leads to emergence of stable, regular Turing patterns formed
around that equilibrium. In this paper we show that coupling reaction-diffusion
equations with ordinary differential equations (ODE) may lead to a novel
pattern formation phenomenon in which DDI causes destabilization of both
constant solutions and Turing patterns. Bistability and hysteresis effects in
the null sets of model nonlinearities yield formation of far from the
equilibrium patterns with jump discontinuity. We derive conditions for
stability of stationary solutions with jump discontinuity in a suitable
topology which allows disclosing the discontinuity points and leads to the
definition of ({\epsilon}0 , A)-stability. Additionally, we provide conditions
on stability of patterns in a quasi-stationary model reduction. The analysis is
illustrated on the example of three-component model of receptor-ligand binding.
The proposed model provides an example of a mechanism of de novo formation of
far from the equilibrium patterns in reaction-diffusion-ODE models involving
co-existence of DDI and hysteresis.
