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Strong resonance and chaos in a single-species chemostat model with periodic pulsing of resource

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  • Toth, Damon J.A.

Abstract

In a single-species chemostat model, oscillations caused by age structure interact with periodic pulsing of the limiting resource to cause a variety of qualitative dynamics. The underlying stroboscopic map, simulated by sampling numerical solutions periodically at the forcing frequency, undergoes a discrete Hopf or Neimark–Sacker bifurcation near the region of parameter space where limit cycles occur in the non-pulsed model. Strong resonance occurs, giving rise to periodic cycles of three or four times the forcing period that dominate over large regions of parameter space. The system also has quasiperiodic solutions, weakly resonant periodic solutions of periods more than four times the forcing period, and chaotic strange attractors arising from period-doubling cascades. Attractors can coexist for a given set of parameters, suggesting that perturbing an age-structured population living in a periodic environment could change the long-term behavior of the population trajectory.

Suggested Citation

  • Toth, Damon J.A., 2008. "Strong resonance and chaos in a single-species chemostat model with periodic pulsing of resource," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 55-69.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:55-69
    DOI: 10.1016/j.chaos.2006.12.001
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    1. Zhang, Yujuan & Xiu, Zhilong & Chen, Lansun, 2005. "Chaos in a food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 159-166.
    2. Lutz Becks & Frank M. Hilker & Horst Malchow & Klaus Jürgens & Hartmut Arndt, 2005. "Experimental demonstration of chaos in a microbial food web," Nature, Nature, vol. 435(7046), pages 1226-1229, June.
    3. Wang, Fengyan & Zhang, Shuwen & Chen, Lansun & Sun, Lihua, 2006. "Bifurcation and complexity of Monod type predator–prey system in a pulsed chemostat," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 447-458.
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    1. San Martín, Jesús & Moscoso, Ma José & González Gómez, A., 2009. "The universal cardinal ordering of fixed points," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1996-2007.

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