The effect of subdiffusion on the stability of autocatalytic systems. (16th January 2023) - Kumar, Uttam; Pushpavanam, Subramaniam
Highlights: Stability of subdiffusive systems exhibiting quadratic and cubic autocatalysis. A robust implicit method based on L 1 scheme for subdiffusive nonlinear systems. A framework to determine Turing patterns in subdiffusive systems is introduced. Classification of bifurcation diagrams for regular and subdiffusive system. Abstract: Many natural phenomena involving physical, chemical and biological processes are subdiffusive in nature. Mathematically these are governed by fractional-order differential equations. The mean square displacement of molecules here scales as t γ, where 0 < γ < 1 . A two-variable system governed by a combination of quadratic and cubic autocatalytic reactions in a porous media is analysed in this work. Here each reactant is involved in the autocatalytic generation of the other. In this work, we investigate the effect of subdiffusion on the stability of the steady-states of the system. Critical surfaces are identified across which the bifurcation diagrams vary. We also developed a methodology to determine regions where Turning patterns can be observed in parameter space. The behaviour in the different regions is verified by a robust implicit numerical method developed for nonlinear systems based on the L 1 scheme. We find that subdiffusive effects increase the region of dynamic stability of the system.