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Published on: June 8, 2018
Stochastic phase transition operator
1Hokkaido University School of Medicine, North 15, West 7, Kita-ku, Sapporo 060-8638, Japan. yamanobe@med.hokudai.ac.jp
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.
- * 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.
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