Oscillations in a plasmid turbidostat model with delayed feedback control

Sanling Yuan; Yongli Song; Junhui Li

doi:10.3934/dcdsb.2011.15.893

Article Contents

2011, Volume 15, Issue 3: 893-914. Doi: 10.3934/dcdsb.2011.15.893

This issue Previous Article Phase transitions of a phase field model Next Article Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology

Oscillations in a plasmid turbidostat model with delayed feedback control

1.
College of Science, Shanghai University for Science and Technology, Shanghai 200093
2.
Department of Mathematics, Tongji University, Shanghai 200092
3.
R&D department, shanghai RAAS blood products Co,. Ltd, Shanghai 200245

Received: January 31, 2010

Revised: August 31, 2010

Published: September 2011

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Abstract

A model of competition between plasmid-bearing and plasmid-free organisms in a turbidostat with delayed feedback control is investigated. By choosing the delay in the measurement of the optical sensor to the turbidity of the fluid as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Computer simulations illustrate the results.

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Mathematics Subject Classification: Primary: 92A15, 34K45; Secondary: 37G15, 92C45.

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