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Singular Perturbation Techniques and Asymptotic Expansions for Some Complex Enzyme Reactions

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Nonlinear Dynamics of Structures, Systems and Devices

Abstract

We summarize some recent results concerning the study of the asymptotic properties of four important enzyme reactions, which are ubiquitous in every intracellular enzyme reaction network. Mainly following the fundamental ideas by Nayfeh, after ad hoc adimensionalizations, we apply classical singular perturbation techniques in order to determine the matched expansions of the solutions, in terms of a suitable parameter, up to the first order. We show some numerical results, for the different mechanisms and different parameter values.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Sapienza University, Roma, Italy

    Alberto Maria Bersani

  2. Institute for System Analysis and Computer Science “Antonio Ruberti”, Roma, Italy

    Alessandro Borri

  3. Department of Basic and Applied Sciences for Engineering, Sapienza University, Roma, Italy

    Alessandro Milanesi & Giovanna Tomassetti

  4. Department of Economics, Roma Tre University, Rome, Italy

    Pierluigi Vellucci

Authors
  1. Alberto Maria Bersani
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  2. Alessandro Borri
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  3. Alessandro Milanesi
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  4. Giovanna Tomassetti
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  5. Pierluigi Vellucci
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Corresponding author

Correspondence to Alberto Maria Bersani .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Walter Lacarbonara

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Balakumar Balachandran

  3. Department of Physics, Lanzhou University of Technology, Lanzhou, Gansu, China

    Jun Ma

  4. Department of Electrical Engineering, Polytechnic of Porto - School of Engineering (ISEP), Porto, Portugal

    J. A. Tenreiro Machado

  5. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gabor Stepan

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Bersani, A.M., Borri, A., Milanesi, A., Tomassetti, G., Vellucci, P. (2020). Singular Perturbation Techniques and Asymptotic Expansions for Some Complex Enzyme Reactions. In: Lacarbonara, W., Balachandran, B., Ma, J., Tenreiro Machado, J., Stepan, G. (eds) Nonlinear Dynamics of Structures, Systems and Devices. Springer, Cham. https://doi.org/10.1007/978-3-030-34713-0_5

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