Saddle-node bifurcation

Stability (learning theory)

Machine learning

Physics

Artificial intelligence

Nonlinear system

Biological applications of bifurcation theory

Quaternion

Geometry

Control (management)

Oscillation (cell signaling)

Bifurcation

Applied mathematics

Mathematics

Computer science

Control theory (sociology)

Artificial neural network

Genetics

Quantum mechanics

Bifurcation theory

Bifurcation diagram

Biology

Neural Networks

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.

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