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Related Concept Videos

Root Loci for Positive-Feedback Systems01:23

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The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Oscillations in delayed positive feedback systems.

Christopher J Ryzowicz1, Richard Bertram1,2,3, Bhargav R Karamched1,2,3

  • 1Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA.

Physical Chemistry Chemical Physics : PCCP
|September 18, 2024
PubMed
Summary
This summary is machine-generated.

Temporal delay in positive feedback loops can generate long-lasting biological oscillations. This finding applies to genetic toggle and one-way switches, challenging existing models of biological rhythm generation.

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Area of Science:

  • Systems biology
  • Biophysics
  • Molecular biology

Background:

  • Positive feedback loops are crucial for biological circuit function.
  • Temporal delays are often considered in negative feedback systems for oscillation generation.

Purpose of the Study:

  • To investigate the impact of temporal delay on the dynamics of canonical positive feedback models.
  • To explore the role of delayed positive feedback in generating biological oscillations.

Main Methods:

  • Mathematical modeling of genetic toggle and one-way switches with delayed feedback.
  • Analysis of transient oscillation duration based on delay magnitude and initial conditions.
  • Application of models to biological systems like Cdc2-Cyclin B/Wee1 and genetic regulatory networks.

Main Results:

  • Long-lasting transient oscillations were observed in both models under general conditions.
  • Oscillation duration is significantly influenced by the magnitude of temporal delay and initial conditions.
  • Demonstrated the existence of long-lasting oscillations in specific biological examples.

Conclusions:

  • Delayed positive feedback systems can generate oscillations, challenging the canonical view of negative feedback systems.
  • Temporal delays in positive feedback loops are a viable mechanism for generating biological oscillations.
  • Findings have implications for understanding biological rhythms and designing synthetic biological circuits.