The nonequilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable fixed point at one-loop order, and the asymptotic scaling of the correlation functions is predicted for both spatial and temporally correlated noise sources. New ...

This project studies the nonhomogeneous steady-state solutions of the Gray-Scott model, a system of nonlinear partial differential equations that has received attention in the past decade in the context of pattern formation and morphogenesis. Morphogenesis, or ‘birth of shape’, is the biological term for the initial formation of patterns that occur in development as cells begin to differentiate...

We introduce a technique based on algebraic topology for quantifying spatio-temporally chaotic dynamics. The technique is illustrated using the Gray-Scott and the FitzHugh-Nagumo models.

Most of the previous studies on well-known Gray-Scott model view it as an irreversible chemical reaction system. In this paper, we derive a four-species reaction-diffusion system using energetic variational approach based law mass action. This is reversible type model, which has natural entropy structure. We establish local well-posedness system, and justify limit to corresponding some backward...

A new geometrical understanding for the spatio-temporal chaos arising in the Gray-Scott model is presented. This is based on the interrelationship of global bifurcating branches of stationary patterns with respect to the supplying and removal rates contained in the model, especially their locations of saddle-node points and the Hopf bifurcation point of a constant state play a key role. It is p...

In this work, we analyze the linear stability of singular homoclinic stationary solutions and spatially periodic stationary solutions in the one-dimensional Gray-Scott model. This stability analysis has several implications for understanding the recently discovered phenomena of self-replicating pulses. For each solution constructed in A. Doelman et al. [Nonlinearity 10 (1997) 523-563], we analy...