Acta Mechanica Sinica

, Volume 31, Issue 2, pp 216–222 | Cite as

Noise-induced bistable switching dynamics through a potential energy landscape

  • Yuanhong Bi
  • Zhuoqin YangEmail author
  • Xiangying Meng
  • Qishao Lu
Research Paper


Interlinked positive feedback loops, an important building block of biochemical systems, can induce bistable switching, leading to long-lasting state changes by brief stimuli. In this work, prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits. A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength, and bistability appears for the moderate feedback strength at a certain noise level. Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.

Graphical Abstract

Prevalent mutual activation between two species A and B as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits. A stochastic fluctuation of the positive feedback strength is introduced to investigate noise-induced bistable switching dynamics in a bistable interval of the positive feedback strength. Stability analysis based on the potential energy landscape is used to explore the noise-induced switching behavior of these two stable steady states.


Stability Bifurcation Noise Bistable switching Potential energy landscape 



The authors thank Dr. Jinzhi Lei for his insights and helpful discussions. This work was supported by the National Natural Science Foundation of China (Grants 11372017, 11272024, and 11371046) and the General Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region (Grant NJZY14130).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Yuanhong Bi
    • 1
    • 2
  • Zhuoqin Yang
    • 1
    Email author
  • Xiangying Meng
    • 3
  • Qishao Lu
    • 4
  1. 1.School of Mathematics and Systems Science and LMIBBeihang UniversityBeijingChina
  2. 2.School of Statistics and MathematicsInner Mongolia University of Finance and EconomicsHohhotChina
  3. 3.Department of BiologyCollege Park University of MarylandMarylandUSA
  4. 4.Department of Dynamics and ControlBeihang UniversityBeijingChina

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