Bifurcation anti‐control technique in a fractional‐order stable finance model

Abstract

Setting up differential models to give a description of the object economical phenomenon in the world today is very essential in economics and mathematics. In this current study, we are committed to the study on the anti‐control of Hopf bifurcation for a fractional‐order stable finance model. By virtue of a suitable washout filter controller involving time delay, we obtain a fractional‐order controlled finance model. Selecting the time delay as bifurcation parameter, we derive a new delay‐independent stability and bifurcation condition to assure that the involved fractional‐order controlled finance model is locally asymptotically stable and generates Hopf bifurcation around the equilibrium point. The investigation clearly manifests that the designed washout filter controller is a very effective means of bifurcation anti‐control. Ultimately, the obtained simulation figures and bifurcation diagrams are sufficiently presented to verify effectiveness for the proposed control technique. The established theoretical fruits have great significance in maintaining financial balance. Up to the present, the report on anti‐control technique of Hopf bifurcation for fractional‐order dynamical systems is quite rare. The research idea can also be applied to probe into the control issue of bifurcation and chaos for numerous other fractional‐order dynamical models in many areas.

Exploration and Control of Bifurcation in a Fractional-Order Delayed Glycolytic Oscillator Model

“…Besides, dominating the stability region and the time of occurrence of Hopf bifurcation of fractional-order dynamical systems is still a valuable work. Nowadays, some excellent works on Hopf bifurcation of fractional-order dynamical systems have been achieved (see [39][40][41][42][43][44]).…”