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Related Experiment Video

Updated: May 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Stochastic phase transition operator.

Takanobu Yamanobe¹

¹Hokkaido University School of Medicine, North 15, West 7, Kita-ku, Sapporo 060-8638, Japan. yamanobe@med.hokudai.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 27, 2011

Summary

A new Markov operator models impulse-driven biological oscillators. This method approximates density evolution and reveals novel stochastic dynamic bifurcations using operator eigenvalues.

Area of Science:

* Mathematical Biology
* Stochastic Processes
* Dynamical Systems

Background:

* Biological oscillators are crucial in various life processes.
* Understanding their dynamics under external impulses is complex.
* Existing methods like Fokker-Planck equations can be computationally intensive.

Purpose of the Study:

* To introduce a novel Markov operator for modeling impulse-driven stochastic biological oscillators.
* To approximate the density evolution of these systems efficiently.
* To analyze oscillator responses and uncover new dynamic behaviors.

Main Methods:

* Construction of a Markov operator's stochastic kernel via asymptotic expansion of stochastic processes.
* Application of the operator to analyze transient and stationary properties.

Related Experiment Videos

Last Updated: May 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

* Utilizing eigenvalues of the product of Markov operators to identify bifurcations.

Main Results:

* The developed Markov operator accurately approximates the density evolution of the biological oscillator.
* The operator facilitates analysis of the oscillator's response to periodic and time-varying impulses.
* An unreported stochastic dynamic bifurcation was discovered using the operator's eigenvalues.

Conclusions:

* The introduced Markov operator provides an effective and efficient tool for studying impulse-driven stochastic biological oscillators.
* This approach offers new insights into oscillator dynamics and bifurcation phenomena.
* The method has potential applications in analyzing complex biological systems with external forcing.