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

Brandibur, Oana; Kaslik, Eva

doi:10.1007/978-981-13-9227-6_5

Cited by 2 publications

(1 citation statement)

References 34 publications

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“…The aim of this work is to complete the stability analysis of twodimensional incommensurate fractional-order systems with Caputo derivatives, by extending the results presented in [4,5]. On one hand, we fully characterize the fractional-order dependent stability and instability properties of the considered system, by exploring certain symmetries related to the characteristic equation associated to our stability problem.…”

Section: Introductionmentioning

confidence: 94%

Exact Stability and Instability Regions for Two-Dimensional Linear Autonomous Multi-Order Systems of Fractional-Order Differential Equations

Brandibur

Kaslik

2021

Fract Calc Appl Anal

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Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and fractional-order-independent stability and instability properties are fully characterised, in terms of the main diagonal elements of the systems’ matrix, as well as its determinant.

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Section: Introductionmentioning

confidence: 94%

Exact Stability and Instability Regions for Two-Dimensional Linear Autonomous Multi-Order Systems of Fractional-Order Differential Equations

Brandibur

Kaslik

2021

Fract Calc Appl Anal

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Stability Results for Two-Dimensional Systems of Fractional-Order Difference Equations

et al. 2020

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Linear autonomous incommensurate systems that consist of two fractional-order difference equations of Caputo-type are studied in terms of their asymptotic stability and instability properties. More precisely, the asymptotic stability of the considered linear system is fully characterized, in terms of the fractional orders of the considered Caputo-type differences, as well as the elements of the linear system’s matrix and the discretization step size. Moreover, fractional-order-independent sufficient conditions are also derived for the instability of the system under investigation. With the aim of exemplifying the theoretical results, a fractional-order discrete version of the FitzHugh–Nagumo neuronal model is constructed and analyzed. Furthermore, numerical simulations are undertaken in order to substantiate the theoretical findings, showing that the membrane potential may exhibit complex bursting behavior for suitable choices of the model parameters and fractional orders of the Caputo-type differences.

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

Cited by 2 publications

References 34 publications

Exact Stability and Instability Regions for Two-Dimensional Linear Autonomous Multi-Order Systems of Fractional-Order Differential Equations

Exact Stability and Instability Regions for Two-Dimensional Linear Autonomous Multi-Order Systems of Fractional-Order Differential Equations

Stability Results for Two-Dimensional Systems of Fractional-Order Difference Equations

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