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Dynamics in piecewise linear and continuous models of complex switching networks

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Listed:
  • Shahrear, Pabel
  • Glass, Leon
  • Wilds, Roy
  • Edwards, Rod

Abstract

Activities of genes are controlled in a combinatorial fashion by the concentrations of chemical called transcription factors. We model this type of network by piecewise linear differential equations formed by embedding a logical switching network in a differential equation. We generate continuous nonlinear equations by replacing the step function discontinuities in the piecewise linear equations by sigmoidal control functions. As the sigmoidal functions become steep, the continuous equations approach piecewise linear differential equations. We carry out numerical studies of the continuous and piecewise linear equations for a 4-dimensional example with particularly interesting and complex behavior, showing that the dynamics in the continuous equation approaches those in the piecewise linear equation as the sigmoids become steep.

Suggested Citation

  • Shahrear, Pabel & Glass, Leon & Wilds, Roy & Edwards, Rod, 2015. "Dynamics in piecewise linear and continuous models of complex switching networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 33-39.
    • Handle: RePEc:eee:matcom:v:110:y:2015:i:c:p:33-39
    DOI: 10.1016/j.matcom.2013.12.002
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    References listed on IDEAS

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    1. Gernot Grabher & Walter W. Powell (ed.), 2004. "Networks," Books, Edward Elgar Publishing, volume 0, number 2771.
    2. Edwards, Roderick & Farcot, Etienne & Foxall, Eric, 2012. "Explicit construction of chaotic attractors in Glass networks," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 666-680.
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    4. Anonymous, 2013. "Introduction to the Issue," Journal of Wine Economics, Cambridge University Press, vol. 8(3), pages 243-243, December.
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