Effect of Advection on the Modified Schnakenberg System

Department of Mathematics, Sebelas Maret University, Jalan Ir. Sutami No. 36A, Kentingan, Jebres, Surakarta 57126, Indonesia

^* Corresponding author: inaas.hmdh29@student.uns.ac.id

Abstract

The Schnakenberg system is a mathematical model that describes the diffusive dynamics of chemical reactions and the formation of space-time patterns. In this paper, we discuss a modified Schnakenberg system including the effects of advection, i.e. reaction diffusion-advection (RDA) system. Stability analysis shows that advection can change the equilibrium state and trigger transitions to complex spatial patterns or oscillatory states. This research uses theoretical analysis methods and literature studies to analyze the impact of diffusion-advection reactions on the modified Schnakenberg system. In this system, only one equilibrium point $S(a+b,\frac{b+{(a+b)}^3}{c{(a+b)}^2})$ is found with the stability condition $b-a<(1+c){(a+b)}^3$. The results also show that advection in the modified Schnakenberg system affects the steady-state stability and have practical implications for understanding bifurcation phenomena in chemical and biological systems.