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Lyapunov-Schmidt reduction and singularity theory analytical techniques are used to study degenerate Hopf bifurcations in a single-species, gas-solid catalytic reaction system. The reactor is assumed to be well mixed and isothermal. The inlet pressure of the reactant is used as a bifurcation parameter. Adsorbate-adsorbate interactions are quantified by a linear increase in activation energy for desorption with coverage. The surface reaction is assumed to require a single site. In spite of the apparent simplicity of the model, the analysis reveals a structure rich in dynamic behavior patterns. The strengths and weaknesses of the analytical methods are discussed in view of the results obtained.