Dynamic Behavior of double-substrate Interactive Model

雙限制基質交互作用下生物反應器之動態分析

吳聲祺(Sheng-Chi Wu) ； 施順雄(Shun-Hsiung Shih) ； 劉懷勝(Hwai-Shen Liu)

《Journal of the Chinese Institute of Chemical Engineers》 38卷2期 (2007/03) Pp. 107-115

摘要

雖然目前常以單一限制基質來描述微生物成長，但微生物總是從環境中攝取多種基質以利生長。因此，將現存的模式延伸到多基質有其實際的必要性。本文以Andrew的基質抑制模式，來探討雙限制基質交互作用下生物反應器之動態行為。模式中的兩個産率因子，一選擇為常數而另一為基質濃度之線性函數、對於所討論的三種情況而言，包括雙限制基質均無抑制、單限制基摶抑制及雙限制基質均有抑制現象，數值分析顯示這三種情況均可得類似的至少三個非零解。其中最高的穩熊總是穩定且可産生最大産量，而最低的穩熊隨著稀釋速率增加從穩定熊變化到非穩定熊，且在轉換過程中出現極限圓。另一個穩熊總是不穩定。對於一或二個基質抑制的情況，産生了第四個穩熊但總是不穩定。

並列摘要

Although modeling microbial growth with one limiting substrate such as Monod model is a common practice, microbes very often consume multiple substances from the environment for their growth. Therefore, the extension of current model to a multi-substrate analysis in needed for practical applications. The dynamic behavior of a double-substrate interactive growth model with Andrew's substrate inhibition model is theoretically discussed in the article. The yield factors considered are either a constant or a linear function of limiting substrate. The simulation indicated that there could be at least three non-trivial steady-state solutions with similar dynamic behavior for all the three cases, i.e. substrate without inhibition, one or both substrate with inhibition. The steady state of highest productivity is always a stable one. The steady state of the lowest productivity could change from a stable mode to an unstable mode while increasing dilution rate. And the limit cycle (sustained oscillation) could appear during the transition. The other steady state is always unstable. For the cases of one or both limiting substrates inhibition, the fourth steady state could appear, and it is always unstable.

並列關鍵字

Microbial growth ； Modeling ； Double-substrate ； Dynamic behavior