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Related Experiment Videos

Hidden oscillations in generalized linear mammaillary compartmental models.

J T Fagarasan, J J Distefano

    Mathematical Biosciences
    |March 1, 1989
    PubMed
    Summary

    Complex eigenvalues in compartmental models can cause hidden oscillations. This study presents a class of models where these oscillations are sometimes visible and sometimes completely hidden in the output, depending on input/output configurations.

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    Area of Science:

    • Mathematical modeling
    • Systems biology
    • Control theory

    Background:

    • Compartmental models are widely used to represent dynamic systems.
    • Oscillations arising from complex eigenvalues can be difficult to detect.
    • These oscillations may be entirely masked in model outputs under certain configurations.

    Purpose of the Study:

    • To construct and analyze a class of linear compartmental models exhibiting hidden oscillations.
    • To investigate the conditions under which these oscillations become visible or remain hidden in the output.
    • To provide an example relevant to biological processes like protein synthesis.

    Main Methods:

    • Definition of generalized mammillary compartmental models with peripheral clusters.
    • Calculation of transfer functions for various single-pool-input/single-pool-output (SpISpO) configurations.

    Related Experiment Videos

  • Analysis of eigenvalue visibility in repetitive generalized mammillary models.
  • Derivation of sufficient conditions for oscillation visibility.

    • Main Results:

    • A class of linear compartmental models with complex eigenvalues was constructed.
    • Demonstrated that oscillating modes can appear in the output for some SpISpO configurations but be totally hidden in others.
    • Identified conditions for oscillation visibility in repetitive generalized mammillary models.
    • Presented a specific model class structurally analogous to nonlinear models of protein synthesis.

    Conclusions:

    • Oscillations in compartmental models can be configuration-dependent, being either observable or completely hidden.
    • The visibility of eigenvalues is crucial for understanding model dynamics.
    • The findings offer insights into the behavior of complex systems, including those modeling biological processes.