Dynamical properties of a fractional reaction-diffusion trimolecular biochemical model with autocatalysis

*Correspondence: [email protected]; [email protected] 1School of Sciences, Nanchang University, Nanchang, 330031, P.R. China 2Numerical Simulation and High-Performance Computing Laboratory, Nanchang University, Nanchang, 330031, P.R. China Abstract In this paper, a reaction-diffusion trimolecular biochemical model with autocatalysis and fractional-order derivative is proposed. We establish the existence and uniqueness of a positive solution to this system in a Besov space. Besides, for this system, we obtain stability, Hopf and Turing bifurcations and spatial patterns. These dynamic behaviors of this system are slightly different from those of its corresponding first-order system. The difference is illustrated by performing some numerical simulations, through which our main results are verified.