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<p>For the discrete-time dynamical system generated by the Poincaré map <i>T</i> of a time-periodic closed-loop negative feedback system, we present an amenable condition which enables us to obtain the global convergence of the orbits. This yields the global convergence to the harmonic periodic solutions of the corresponding time-periodic systems with negative feedback. Our approach is motivated by embedding the negative feedback system into a larger time-periodic monotone dynamical systems. We further utilize the theoretical results to obtain the global convergence to periodic solutions for the time periodically forced gene regulatory models. Numerical simulations are exhibited to illustrate the feasibility of our theoretical results for this model.</p>

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Global Convergence for Time-periodic Systems with Negative Feedback and Applications

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Yi Wang,
  • Wenji Wu,
  • Hui Zhou

摘要

For the discrete-time dynamical system generated by the Poincaré map T of a time-periodic closed-loop negative feedback system, we present an amenable condition which enables us to obtain the global convergence of the orbits. This yields the global convergence to the harmonic periodic solutions of the corresponding time-periodic systems with negative feedback. Our approach is motivated by embedding the negative feedback system into a larger time-periodic monotone dynamical systems. We further utilize the theoretical results to obtain the global convergence to periodic solutions for the time periodically forced gene regulatory models. Numerical simulations are exhibited to illustrate the feasibility of our theoretical results for this model.