Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction

•Lie symmetries generators for oscillatory Belousov–Zhabotinsky reaction.•The optimal system of sub-algebras.•The power series solution and graphical illustration.•The modulational instability constraint for the mathematical Noyes–Field Model.•The graphical visualization of gain spectrum.