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Microbial predation in coupled chemostats: A global study of two coupled nonlinear oscillators. (English) Zbl 0802.92028

Summary: Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When two such chemostats interact through flow exchange, the interplay of the oscillation frequencies gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions between them as the coupling strength and relative frequencies of the two chemostats vary. We concentrate on certain strong resonance phenomena between the two frequencies as well as their mutual extinction and provide a representative sampling of possible phase portraits for our model system.
Our observations corroborate recent mathematical results and case studies of coupled nonlinear chemical oscillators in which regions of mutual extinction as well as the Arnol’d structure for two-parameter families of maps of the plane have been observed. We highlight certain unexpected features of the operating diagram discovered through our computational study and discuss their implication for the dynamic response of the chemostat system.

MSC:

92D40 Ecology
65L07 Numerical investigation of stability of solutions to ordinary differential equations
65L99 Numerical methods for ordinary differential equations

Software:

ODESSA; AUTO-86; AUTO
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Full Text: DOI

References:

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