Novel bifurcation results for a delayed fractional-order quaternion-valued neural network

Abstract

This paper reports the innovative results on the stability and bifurcation for a delayed fractional-order quaternion-valued neural network(FOQVNN). Delay-stimulated bifurcation criteria of the developed FOQVNN are attained. Then, the bifurcation diagrams are perfectly exhibited to authenticate the veracity of the bifurcation results. Besides, the stability zone is more larger of the addressed FOQVNN in comparison with its counterpart if other parameters are intercalated. It further witnesses that the amplitudes of bifurcation oscillation get bigger with the augmentation of time delay. It discloses that the bifurcation phenomena engender earlier as the order incrementally magnifies. The exactness and merits of the achieved analytic results are eventually substantiated by a simulation example.

Keywords: Fractional order; Hopf bifurcation; Neural networks; Quaternion-valued; Time delay.