# Synchronization of Biological Oscillators

## Location

CSU 202

## Start Date

27-4-2009 10:00 AM

## End Date

27-4-2009 12:00 PM

## Student's Major

Mathematics and Statistics

## Student's College

Science, Engineering and Technology

## Mentor's Name

Namyong Lee

## Mentor's Department

Mathematics and Statistics

## Mentor's College

Science, Engineering and Technology

## Second Mentor's Name

Anne-Marie Hoskinson

## Second Mentor's Department

Biological Sciences

## Second Mentor's College

Science, Engineering and Technology

## Description

Many biological systems consisting of a population of oscillators exhibit self-synchronization. In such populations, components that naturally behave periodically respond in some way to oscillations of other components. Each individual has its own natural frequency but is capable of adjusting its frequency according to the frequencies of the other individuals in the population. The phase position of a particular oscillator determines how influential it is on other oscillators via an "influence function". An oscillator's current phase position also determines how sensitive it is to other oscillators according to a "sensitivity function". With the assumption that every oscillator in a population has the same influence and sensitivity functions, we constructed a system of differential equations to model each oscillator's rate of change of phase position. We also assumed a normal distribution of natural frequencies across the population. We found that under certain conditions, large numbers of oscillators become synchronized almost spontaneously. This phenomenon can be seen in some populations of fireflies who synchronize their flashing, in the pacemaker cells of the heart, and in certain types of neurons just to name a few examples. In a sense, we witness the emergence of order out of a chaotic system.

Synchronization of Biological Oscillators

CSU 202

Many biological systems consisting of a population of oscillators exhibit self-synchronization. In such populations, components that naturally behave periodically respond in some way to oscillations of other components. Each individual has its own natural frequency but is capable of adjusting its frequency according to the frequencies of the other individuals in the population. The phase position of a particular oscillator determines how influential it is on other oscillators via an "influence function". An oscillator's current phase position also determines how sensitive it is to other oscillators according to a "sensitivity function". With the assumption that every oscillator in a population has the same influence and sensitivity functions, we constructed a system of differential equations to model each oscillator's rate of change of phase position. We also assumed a normal distribution of natural frequencies across the population. We found that under certain conditions, large numbers of oscillators become synchronized almost spontaneously. This phenomenon can be seen in some populations of fireflies who synchronize their flashing, in the pacemaker cells of the heart, and in certain types of neurons just to name a few examples. In a sense, we witness the emergence of order out of a chaotic system.

#### Recommended Citation

Wuollet, Joshua and Jesse Feller. "Synchronization of Biological Oscillators." *Undergraduate Research Symposium*, Mankato, MN, April 27, 2009.

https://cornerstone.lib.mnsu.edu/urs/2009/oral-session-05/5