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

Department of Applied Mathematics, Western University, London, Ontario, N6A 5B7, Canada

Special Issues: Recent Advances in Mathematical Population Dynamics

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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Keywords Slow-fast motion; oscillating network; organic reaction; sustained oscillation; recurrence; stability and bifurcation; saddle-node bifurcation; Hopf bifurcation; limit cycle

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


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