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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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DOI

10.1002/ar.21397

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1573-269X

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The Routh–Hurwitz conditions of fractional type in

Authors: Jan Čermák Luděk Nechvátal
Publish Date: 2016/09/24
Volume: 87, Issue: 2, Pages: 939-954
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Abstract

This paper discusses stability conditions and a chaotic behavior of the Lorenz dynamical system involving the Caputo fractional derivative of orders between 0 and 1 Contrary to some existing results on the topic we study these problems with respect to a general not specified value of the Rayleigh number as a varying control parameter Such a bifurcation analysis is known for the classical Lorenz system we show that analysis of its fractional extension can yield different conclusions In particular we theoretically derive and numerically illustrate that nontrivial equilibria of the fractional Lorenz system become locally asymptotically stable for all values of the Rayleigh number large enough which contradicts the behavior known from the classical case As a main proof tool we derive the optimal Routh–Hurwitz conditions of fractional type ie necessary and sufficient conditions guaranteeing that all zeros of the corresponding characteristic polynomial are located inside the Matignon stability sector Beside it we perform other bifurcation investigations of the fractional Lorenz system especially those documenting its transition from stability to chaotic behavior

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