Applications of the Belousov–Zhabotinsky reaction–diffusion system: Analytical and numerical approaches

Abstract The Belousov–Zhabotinsky (BZ) reaction–diffusion system is a well-known model of chemical self-organization that exhibits complex spatiotemporal patterns. The BZ reaction–diffusion system provides a useful tool for studying the behavior of waves in random and complex media. Its applications in this field are wide-ranging and have the potential to contribute to a better understanding of the behavior of waves in natural and engineered systems. In this article, we investigate the BZ system using both analytical and numerical methods. We first apply the Bernoulli sub-ordinary differential equation (ODE) technique to the BZ system to obtain a simplified system of ODEs. Then, we use the exponential cubic B-spline method and the trigonometric cubic B-spline method to solve the simplified system numerically. The results show that both methods are effective in capturing the essential features of the BZ system. We also compare the results obtained using the two numerical methods. Our findings analytically contribute to a better understanding of the BZ system through graphs of the soliton solutions.