MBI Publications

MBI Publications for Maria Leite (2)

  • M. Aguiar, M. Aguiar, A. Dias, A. Dias, M. Golubitsky and M. Leite
    Bifurcations from regular quotient networks: A first insight
    Physica D.Vol. 238 No. 2 (2009) pp. 137-155


  • M. Leite and Y. Wang
    Multistability, Oscillations and Bifurcations in Feedback Loops.
    Math. Biosci. EngVol. 7 No. 1 (2010) pp. 83-97


    Feedback loops are found to be important network structures in

    regulatory networks of biological signaling systems because they are responsi-

    ble for maintaining normal cellular activity. Recently, the functions of feedback

    loops have received extensive attention. The existing results in the literature

    mainly focus on verifying that negative feedback loops are responsible for oscil-

    lations, positive feedback loops for multistability, and coupled feedback loops

    for the combined dynamics observed in their individual loops. In this work,

    we develop a general framework for studying systematically functions of feed-

    back loops networks. We investigate the general dynamics of all networks with

    one to three nodes and one to two feedback loops. Interestingly, our results

    are consistent with Thomasâ?? conjectures although we assume each node in the

    network undergoes a decay, which corresponds to a negative loop in Thomasâ??

    setting. Besides studying how network structures influence dynamics at the

    linear level, we explore the possibility of network structures having impact on

    the nonlinear dynamical behavior by using Lyapunov-Schmidt reduction and

    singularity theory.

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