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On the Phase Portrait Phase Portrait of the System \({{\dot x} = {Ax} + {\langle a, x\rangle x}}\)

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Abstract

Structure of the phase space of the nonlinear system \({{\dot {\varvec x} = {\varvec Ax} + {\langle {\varvec a}, {\varvec x}\rangle {\varvec x}}}}\) is clarified using saddle-node bifurcations \({{{\varvec x}, {\varvec a} \in \mathbb{R}^d,}}\) is a d × d-matrix).

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Authors and Affiliations

  1. Institute of Mathematics and Information Technologies, Durmon yuli st. 29, 100125, Tashkent, Uzbekistan

    Abdulla Azamov & Dilmurod Boytillaev

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  1. Abdulla Azamov
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  2. Dilmurod Boytillaev
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Correspondence to Abdulla Azamov.

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Azamov, A., Boytillaev, D. On the Phase Portrait Phase Portrait of the System \({{\dot x} = {Ax} + {\langle a, x\rangle x}}\) . Qual. Theory Dyn. Syst. 11, 467–479 (2012). https://doi.org/10.1007/s12346-012-0078-9

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  • DOI: https://doi.org/10.1007/s12346-012-0078-9

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