Oscillations in a plasmid turbidostat model with delayed feedback control

Pages: 893 - 914, Volume 15, Issue 3, May 2011

doi:10.3934/dcdsb.2011.15.893       Abstract        References        Full Text (1251.0K)       Related Articles

Sanling Yuan - College of Science, Shanghai University for Science and Technology, Shanghai 200093, China (email)
Yongli Song - Department of Mathematics, Tongji University, Shanghai 200092, China (email)
Junhui Li - R&D department, shanghai RAAS blood products Co,. Ltd, Shanghai 200245, China (email)

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.

Keywords:  Time delay, turbidostat, Hopf bifurcation, stability, periodic solution.
Mathematics Subject Classification:  Primary: 92A15, 34K45; Secondary: 37G15, 92C45.

Received: February 2010;      Revised: September 2010;      Published: February 2011.

 References