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Purpose <p>Bio-inspired oscillators can offer efficient structural performance to meet the requirements of engineering problems. Meanwhile, due to the birhythmicity of biology, they also possess the characteristics of fast-slow and time delay. However, many studies did not take into account their effect on the system. In order to find the performance, this paper explores the bifurcation and bursting patterns in a bio-inspired nonlinear oscillator under slow externally excitation and time delay. We conduct the bifurcation analysis as well as derive the conditions of fold and Hopf bifurcation.</p> Method <p>The stability of equilibrium point is discussed by utilizing the eigenvalue theory of linearized systems. Moreover, the mechanism of bursting oscillation is revealed by employing transformed phase trajectory.</p> Results <p>The symmetric fold-fold bursting and symmetric Hopf-Hopf bursting are identified by tuning the time-delay gain coefficient and the time-delay. In particular, the symmetric double-Hopf/double-Hopf bursting is observed under certain time-delay parameter conditions.</p>

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Compound Bursting of a Bio-inspired Nonlinear Oscillator Under Fast-slow Excitation and Time Delay

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Miaorong Zhang,
  • Wenan Jiang,
  • Qinsheng Bi,
  • Liqun Chen

摘要

Purpose

Bio-inspired oscillators can offer efficient structural performance to meet the requirements of engineering problems. Meanwhile, due to the birhythmicity of biology, they also possess the characteristics of fast-slow and time delay. However, many studies did not take into account their effect on the system. In order to find the performance, this paper explores the bifurcation and bursting patterns in a bio-inspired nonlinear oscillator under slow externally excitation and time delay. We conduct the bifurcation analysis as well as derive the conditions of fold and Hopf bifurcation.

Method

The stability of equilibrium point is discussed by utilizing the eigenvalue theory of linearized systems. Moreover, the mechanism of bursting oscillation is revealed by employing transformed phase trajectory.

Results

The symmetric fold-fold bursting and symmetric Hopf-Hopf bursting are identified by tuning the time-delay gain coefficient and the time-delay. In particular, the symmetric double-Hopf/double-Hopf bursting is observed under certain time-delay parameter conditions.