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Oscillatory dynamics of the biologically active zone in in situ bioremediation
Author(s) -
Murray Regan E.,
Luce Benjamin P.
Publication year - 2002
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2000wr000206
Subject(s) - bioremediation , hopf bifurcation , oscillation (cell signaling) , bifurcation , partial differential equation , biological system , parametric statistics , delay differential equation , differential equation , mathematics , physics , chemistry , contamination , ecology , biology , nonlinear system , mathematical analysis , statistics , biochemistry , quantum mechanics
In situ bioremediation is a promising biotechnology for removing aqueous phase contaminants from groundwater. The system of three partial differential equations used to model bioremediation has a traveling wave solution which loses stability in a Hopf bifurcation, giving rise to oscillating fronts. To understand the origin of these oscillations, we construct a simplified model of the biologically active zone, a time delay differential equation with state‐dependent delay. Despite its simplicity the new model mimics the dynamical characteristics of the bioremediation equations remarkably well and yields an approximate parametric expression for the oscillation onset point.