Lecture

Entrainment and Synchronization of Oscillators

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In course

BIO-341: Dynamical systems in biology

Life is non-linear. This course introduces dynamical systems as a technique for modelling simple biological processes. The emphasis is on the qualitative and numerical analysis of non-linear dynamical models. Examples are taken from biology and population ...

Description

This lecture covers the concepts of entrainment and synchronization of oscillators, focusing on the Kuramoto model. It discusses the entrainment of phase oscillators through continuous and pulsed coupling, as well as the collective synchronization in populations of phase oscillators. The lecture explores the resonance phenomena in human circadian rhythms and the Kuramoto model for synchronization. It delves into the dynamics of phase oscillators and the effect of external stimuli on oscillatory systems. The training notes analyze different cases of entrainment and stability in oscillatory systems, providing insights into the behavior of coupled biological oscillators.

Instructors (2)

Felix Naef

Felix Naef studied theoretical physics at the ETHZ and obtained his PhD from the EPFL in 2000. He then received postdoctoral training at the Center for Studies in Physics and Biology at the Rockefeller University (NYC) under the guidance of Prof. Magnasco. His research focuses on the modeling and interpretation of high-throughput functional data and the study of biomolecular oscillators. He joined ISREC as an associate scientist in early 2004 and is currently Associate Professor in the Institute of Bioengineering (IBI).

Julian Charles Shillcock

Julian received his PhD at Simon Fraser University in Canada for work on Monte Carlo simulations of liquid crystal phase transitions and the elastic properties of fluid and polymerized membranes. He was a Group Leader at the Max Planck Institute of Colloids and Interfaces, Germany for five years applying coarse-grained simulation techniques - principally Dissipative Particle Dynamics (DPD) and Brownian Dynamics - to equilibrium and dynamic properties of fluid lipid membranes. A major target of this research was to reveal the molecular rearrangements that occur during vesicle fusion. During this time, he developed a commercially-available, parallel DPD code that is being used by several universities. He was an Associate Professor at MEMPHYS in the Department of Physics and Chemistry, University of Southern Denmark. He has also worked in industry, designing and writing software for communication satellite simulations (British Aerospace, 1986-1990), and fluid simulation software (Accelrys, Inc., 1998-1999). He joined the Blue Brain Project in 2011, and uses mesoscale simulation techniques, together with theoretical analysis and collaborations with experimentalists, to study the dynamics of cellular processes. Current projects include simulating the formation of the post-synaptic density in dendritic spines and developing theoretical models of the supramolecular organisation of synapses. He also teaches Master's and PhD courses in computational cell biology and biophysics. He wrote and maintains an open source dissipative particle dynamics simulation code: https://github.com/Osprey-DPD/osprey-dpd Orcid: orcid.org/0000-0002-7885-735X

Official source

Related concepts (32)

Oscillation

Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms.

Circadian clock

A circadian clock, or circadian oscillator, is a biochemical oscillator that cycles with a stable phase and is synchronized with solar time. Such a clock's in vivo period is necessarily almost exactly 24 hours (the earth's current solar day). In most living things, internally synchronized circadian clocks make it possible for the organism to anticipate daily environmental changes corresponding with the day–night cycle and adjust its biology and behavior accordingly.

Circadian rhythm

A circadian rhythm (sərˈkeɪdiən), or circadian cycle, is a natural oscillation that repeats roughly every 24 hours. Circadian rhythms can refer to any process that originates within an organism (i.e., endogenous) and responds to the environment (is entrained by the environment). Circadian rhythms are regulated by a circadian clock whose primary function is to rhythmically co-ordinate biological processes so they occur at the correct time to maximise the fitness of an individual.

Electronic oscillator

An electronic oscillator is an electronic circuit that produces a periodic, oscillating or alternating current (AC) signal, usually a sine wave, square wave or a triangle wave, powered by a direct current (DC) source. Oscillators are found in many electronic devices, such as radio receivers, television sets, radio and television broadcast transmitters, computers, computer peripherals, cellphones, radar, and many other devices.

Harmonic oscillator

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x: where k is a positive constant. If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).

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