Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Note on the Local Stability Theory for Caputo Fractional Planar System

Version 1 : Received: 7 October 2020 / Approved: 8 October 2020 / Online: 8 October 2020 (13:00:38 CEST)

How to cite: Hoti, M. A Note on the Local Stability Theory for Caputo Fractional Planar System. Preprints 2020, 2020100175 (doi: 10.20944/preprints202010.0175.v1). Hoti, M. A Note on the Local Stability Theory for Caputo Fractional Planar System. Preprints 2020, 2020100175 (doi: 10.20944/preprints202010.0175.v1).

Abstract

In this manuscript a new approach into analyzing the local stability of equilibrium points of non-linear Caputo fractional planar systems is shown. It is shown that the equilibrium points of such systems can be a stable focus or unstable focus. In addition, it is proposed that previous results regarding the stability of equilibrium points have been incorrect, the results here attempt to correct such results. Lastly, it is proposed that a Caputo fractional planar system cannot undergo a Hopf bifurcation, contrary to previous results prior. Though, it is shown that such systems can undergo a Hopf bifurcation (topologically).

Subject Areas

Caputo derivative; Stability,; Hopf Bifurcation

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