Stability and bifurcation analysis of a fractional order delay differential equation involving cubic nonlinearity

Sachin Bhalekar and Deepa Gupta

Chaos, Solitons & Fractals, 2022, vol. 162, issue C

Abstract: Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation Dαx(t)=δx(t−τ)−ϵx(t−τ)3−px(t)2+qx(t).We provide linearization of this system in a neighborhood of equilibrium points and propose linearized stability conditions. To discuss the stability of equilibrium points, we propose various conditions on the parameters δ, ϵ, p, q and τ. Even though there are five parameters involved in the system, we are able to provide the stable region sketch in the qδ−plane for any positive ϵ and p. This provides the complete analysis of stability of the system. Further, we investigate chaos in the proposed model. This system exhibits chaos for a wide range of delay parameter.

Keywords: Delay; Fractional derivative; Stability; Chaos (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006890

DOI: 10.1016/j.chaos.2022.112483

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