Detail publikace

On a problem of linearized stability for fractional difference equations

ČERMÁK, J. NECHVÁTAL, L.

Originální název

On a problem of linearized stability for fractional difference equations

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

This paper discusses the problem of linearized stability for nonlinear fractional difference equations. Computational methods based on appropriate linearization theorem are standardly applied in bifurcation analysis of dynamical systems. However, in the case of fractional discrete systems, a theoretical background justifying its use is still missing. Therefore, the main goal of this paper is to fill in the gap. We consider a general autonomous system of fractional difference equations involving the backward Caputo fractional difference operator and prove that any equilibrium of this system is asymptotically stable if the zero solution of the corresponding linearized system is asymptotically stable. Moreover, these asymptotic stability conditions for equilibria of the system are described via location of all the characteristic roots in a specific area of the complex plane. In the planar case, these conditions are given even explicitly in terms of trace and determinant of the appropriate Jacobi matrix. The results are applied to a fractional predator-prey model and the fractional Lorenz model. Related experiments are supported by a numerical code that is appended as well

Klíčová slova

Fractional differential and difference equation; Asymptotic stability; Linearization theorem; Bifurcation

Autoři

ČERMÁK, J.; NECHVÁTAL, L.

Vydáno

5. 4. 2021

Nakladatel

SPRINGER

Místo

DORDRECHT

ISSN

1573-269X

Periodikum

NONLINEAR DYNAMICS

Ročník

104

Číslo

2

Stát

Spojené státy americké

Strany od

1253

Strany do

1267

Strany počet

15

URL

https://link.springer.com/article/10.1007/s11071-021-06372-9

BibTex

@article{BUT171521,
  author="Jan {Čermák} and Luděk {Nechvátal}",
  title="On a problem of linearized stability for fractional difference equations",
  journal="NONLINEAR DYNAMICS",
  year="2021",
  volume="104",
  number="2",
  pages="1253--1267",
  doi="10.1007/s11071-021-06372-9",
  issn="1573-269X",
  url="https://link.springer.com/article/10.1007/s11071-021-06372-9"
}