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Dynamics of the Higgins–Selkov and Selkov systems

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  • Artés, Joan Carles
  • Llibre, Jaume
  • Valls, Claudià

Abstract

We describe the global dynamics in the Poincaré disc of the Higgins–Selkov model x′=k0−k1xy2,y′=−k2y+k1xy2,where k0, k1, k2 are positive parameters, and of the Selkov model x′=−x+ay+x2y,y′=b−ay−x2y,where a, b are positive parameters. We determine the regions of initial conditions with biological meaning.

Suggested Citation

  • Artés, Joan Carles & Llibre, Jaume & Valls, Claudià, 2018. "Dynamics of the Higgins–Selkov and Selkov systems," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 145-150.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:145-150
    DOI: 10.1016/j.chaos.2018.07.007
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    References listed on IDEAS

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    1. Al Noufaey, K.S. & Marchant, T.R., 2014. "Semi-analytical solutions for the reversible Selkov model with feedback delay," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 49-59.
    2. Llibre, Jaume & Makhlouf, Amar, 2016. "Zero-Hopf bifurcation in the generalized Michelson system," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 228-231.
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    Cited by:

    1. Llibre, Jaume & Oliveira, Regilene D.S. & Valls, Claudia, 2019. "Final evolutions for simplified multistrain/two-stream model for tuberculosis and dengue fever," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 181-186.

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