Abstract
We discuss a system of ordinary differential equations that can be used to model the interspecies hydrogen transfer common in anaerobic degradation of organic matter. The mutualistic character of the interaction is not modeled explicitly but emerges as a consequence of the kinetics of nutrient uptake. Using monotonicity assumptions on the reaction terms, we characterise the equilibria and their stability and demonstrate two-parameter bifurcation of periodic solutions near singularities of the Bogdanov-Takens type. We have persistence and extinction results in a wide range of parameter values. Finally, we give some conditions for equivalence and non-equivalence to a cooperative system and compare to related models.
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Burchard, A. Substrate degradation by a mutualistic association of two species in the Chemostat. J. Math. Biol. 32, 465–489 (1994). https://doi.org/10.1007/BF00160169
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DOI: https://doi.org/10.1007/BF00160169