Almost automorphic solutions for Clifford-valued neutral-type fuzzy cellular neural networks with leakage delays on time scales

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

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.

Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays

In this paper, the existence and stability of Weyl almost automorphic solutions in distribution sense for a class of Clifford-valued stochastic neural networks with time-varying delays are studied by using the direct method. Firstly, the existence and uniqueness of Weyl almost automorphic solutions in distribution sense for this class of neural networks are studied by using the Banach fixed point theorem and the relationship between several different senses of random almost automorphy. Then, the global exponential stability in p th mean of the unique Weyl almost automorphic solution in distribution sense is proved by inequality technique and counter proof method. Even when this class of neural networks we consider is real-valued, our results are new. Meanwhile, the method proposed in this paper can be used to study the existence of Weyl almost automorphic solutions of other types of neural networks including stochastic and deterministic neural networks. Finally, an example is given to illustrate the feasibility of our results.