Oscillations are periodic variations that can be found in many physical, chemical and biological systems. Examples include the 24 hour cycle of the earth’s rotation and the biological circadian clock, but also vibrations of guitar strings, our heartbeat, and the cell division cycle.

Biological rhythms are generated by oscillations in the concentration or activity of critical regulators, which can have very different periods. In the case of our heart rate, the sino-atrial node generates 50 to 150 action potentials per minute, depending on the oxygen demands of the body. Similarly, the period of the cell division cycle ranges from 10-30 minutes in rapidly cleaving early embryos to about 10-30 hours in dividing somatic cells.

So far, any (biological) oscillator has been found to require (time-delayed) negative feedback to reset the system after each cycle.

What causes such oscillations?  So far, any (biological) oscillator has been found to require (time-delayed) negative feedback to reset the system after each cycle. As the level of a certain quantity increases over time, after a certain time (delay) the negative feedback kicks in causing the levels to drop again. This then also leads to a decreased feedback, allowing the levels to rise again.

Positive feedback is yet another interaction type that is often found in biological oscillators, as it has been shown to be important to generate robust, large-amplitude oscillations with tunable frequency. At the core of such relaxation oscillations is the fact that positive feedback can generate bistability in the system. A system is called bistable if there are two stable states for the same external conditions (system parameters). In which state the system ends up depends on the initial conditions.

Negative feedback can then drive oscillations along both branches of the bistable response curve. As a result, such relaxation oscillators exist over a wider range of parameters and allow the system to regulate its oscillation frequency without compromising its amplitude.

Relaxation oscillations can result by combining positive and negative feedback loops.

Selected publications



Cebrián-Lacasa, D.; Leda, M.; Goryachev, A. B.; Gelens, L.

Wave-driven phase wave patterns in a ring of FitzHugh-Nagumo oscillators

2024, visited: 23.04.2024.

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Cebrián-Lacasa, D.; Parra-Rivas, P.; Ruiz-Reynés, D.; Gelens, L.

Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines

2024, visited: 17.04.2024.

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Prokop, B.; Gelens, L.

From biological data to oscillator models using SINDy

In: iScience, vol. 27, no. 4, pp. 109316, 2024, ISSN: 2589-0042.

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Prokop, B.; Frolov, N.; Gelens, L.

Enhancing model identification with SINDy via nullcline reconstruction

2024, visited: 06.02.2024.

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Puls*, O.; Ruiz-Reynés*, D.; Tavella, F.; Jin, M.; Kim, Y.; Gelens*, L.; Yang*, Q.

Mitotic waves in frog egg extracts: Transition from phase waves to trigger waves

2024, visited: 23.01.2024.

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Rombouts, J.; Vandervelde, A.; Gelens, L.

Delay models for the early embryonic cell cycle oscillator

In: PLoS One, vol. 13, no. 3, pp. 1-21, 2018.

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Gelens, L.; Qian, J.; Bollen, M.; Saurin, A. T.

The Importance of Kinase–Phosphatase Integration: Lessons from Mitosis

In: Trends in Cell Biology, vol. 28, iss. 1, pp. 6-21, 2017, ISSN: 0962-8924.

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Anderson*, G. A.; Gelens*, L.; Baker, J.; Ferrell, J. E. Jr.

Desynchronizing Embryonic Cell Division Waves Reveals the Robustness of Xenopus laevis Development

In: Cell Reports, vol. 21, iss. 1, pp. 37–46, 2017, (featured on the cover).

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