This study provides semi-analytical solutions to the Selkov-Schnakenberg reaction-diffusion system. The Galerkin method is applied to approximate the system of partial differential equations by a system of ordinary differential equations. The steady states of the system and the limit cycle solutions are delineated using bifurcation diagram analysis. The influence of the diffusion coefficients as they change, on the system stability is examined. Near the Hopf bifurcation point, the asymptotic analysis is developed for the oscillatory solution. The semi-analytical model solutions agree accurately with the numerical results.

中文翻译：

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Selkov-Schnakenberg反应扩散系统的稳定性分析

这项研究为Selkov-Schnakenberg反应扩散系统提供了半解析解。运用Galerkin方法通过常微分方程组逼近偏微分方程组。使用分叉图分析来描绘系统的稳态和极限循环解。研究了扩散系数的变化对系统稳定性的影响。在Hopf分叉点附近，针对振动解进行了渐近分析。半解析模型解与数值结果准确吻合。