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Stability Analysis of Two-Dimensional Incommensurate Systems of Fractional-Order Differential Equations

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Abstract

Recently obtained necessary and sufficient conditions for the asymptotic stability and instability of the null solution of a two-dimensional autonomous linear incommensurate fractional-order dynamical system with Caputo derivatives are reviewed and extended. These theoretical results are then applied to investigate the stability properties of a two-dimensional fractional-order conductance-based neuronal model. Moreover, the occurrence of Hopf bifurcations is also discussed, choosing the fractional orders as bifurcation parameters. Numerical simulations are also presented to illustrate the theoretical results.

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Authors and Affiliations

  1. West University of Timişoara, Bd. V. Pârvan nr. 4, 300223, Timişoara, Romania

    Oana Brandibur & Eva Kaslik

  2. Academy of Romanian Scientists, Splaiul Independenţei 54, 050094, Bucharest, Romania

    Eva Kaslik

  3. Institute e-Austria Timisoara, Bd. V. Pârvan nr. 4, cam. 045B, 300223, Timişoara, Romania

    Eva Kaslik

Authors
  1. Oana Brandibur
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  2. Eva Kaslik
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Correspondence to Eva Kaslik .

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Editors and Affiliations

  1. Department of Mathematics, Savitribai Phule Pune University, Pune, Maharashtra, India

    Varsha Daftardar-Gejji

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Brandibur, O., Kaslik, E. (2019). Stability Analysis of Two-Dimensional Incommensurate Systems of Fractional-Order Differential Equations. In: Daftardar-Gejji, V. (eds) Fractional Calculus and Fractional Differential Equations. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-9227-6_5

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