Research article

Analysis on recurrence behavior in oscillating networks of biologically relevant organic reactions

  • Received: 10 April 2019 Accepted: 14 April 2019 Published: 10 June 2019
  • In this paper, we present a new method based on dynamical system theory to study certain type of slow-fast motions in dynamical systems, for which geometric singular perturbation theory may not be applicable. The method is then applied to consider recurrence behavior in an oscillating network model which is biologically related to organic reactions. We analyze the stability and bifurcation of the equilibrium of the system, and find the conditions for the existence of recurrence, i.e., there exists a "window" in bifurcation diagram between a saddle-node bifurcation point and a Hopf bifurcation point, where the equilibrium is unstable. Simulations are given to show a very good agreement with analytical predictions.

    Citation: Pei Yu, Xiangyu Wang. Analysis on recurrence behavior in oscillating networks of biologically relevant organic reactions[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5263-5286. doi: 10.3934/mbe.2019263

    Related Papers:

  • In this paper, we present a new method based on dynamical system theory to study certain type of slow-fast motions in dynamical systems, for which geometric singular perturbation theory may not be applicable. The method is then applied to consider recurrence behavior in an oscillating network model which is biologically related to organic reactions. We analyze the stability and bifurcation of the equilibrium of the system, and find the conditions for the existence of recurrence, i.e., there exists a "window" in bifurcation diagram between a saddle-node bifurcation point and a Hopf bifurcation point, where the equilibrium is unstable. Simulations are given to show a very good agreement with analytical predictions.


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