New results on bifurcation for fractional-order octonion-valued neural networks involving delays*

ABSTRACT

This work chiefly explores fractional-order octonion-valued neural networks involving delays. We decompose the considered fractional-order delayed octonion-valued neural networks into equivalent real-valued systems via Cayley-Dickson construction. By virtue of Lipschitz condition, we prove that the solution of the considered fractional-order delayed octonion-valued neural networks exists and is unique. By constructing a fairish function, we confirm that the solution of the involved fractional-order delayed octonion-valued neural networks is bounded. Applying the stability theory and basic bifurcation knowledge of fractional order differential equations, we set up a sufficient condition remaining the stability behaviour and the appearance of Hopf bifurcation for the addressed fractional-order delayed octonion-valued neural networks. To illustrate the justifiability of the derived theoretical results clearly, we give the related simulation results to support these facts. Simultaneously, the bifurcation plots are also displayed. The established theoretical results in this work have important guiding significance in devising and improving neural networks.

KEYWORDS:

• Fractional-order octonion-valued neural networks
• existence and uniqueness
• boundedness
• stability
• Hopf bifurcation
• bifurcation diagram

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Science Foundation of China [No.61673008 and No.62062018] and Project of High-level Innovative Talents of Guizhou Province [[2016]5651]