In this study, we investigate the global exponential stability of Clifford-valued neural network (NN) models with impulsive effects and time-varying delays. By taking impulsive effects into consideration, we firstly establish a Clifford-valued NN model with time-varying delays. The considered model encompasses real-valued, complex-valued, and quaternion-valued NNs as special cases. In order to avoid the issue of non-commutativity of the multiplication of Clifford numbers, we divide the originaln-dimensional Clifford-valued model into $2^{m}n$2mn -dimensional real-valued models. Then we adopt the Lyapunov–Krasovskii functional and linear matrix inequality techniques to formulate new sufficient conditions pertaining to the global exponential stability of the considered NN model. Through numerical simulation, we show the applicability of the results, along with the associated analysis and discussion.

This paper considers the Clifford-valued recurrent neural network (RNN) models, as an augmentation of real-valued, complex-valued, and quaternion-valued neural network models, and investigates their global exponential stability in the Lagrange sense. In order to address the issue of non-commutative multiplication with respect to Clifford numbers, we divide the originaln-dimensional Clifford-valued RNN model into $2^{m}n$2mn real-valued models. On the basis of Lyapunov stability theory and some analytical techniques, several sufficient conditions are obtained for the considered Clifford-valued RNN models to achieve global exponential stability according to the Lagrange sense. Two examples are presented to illustrate the applicability of the main results, along with a discussion on the implications.

This paper addresses an adaptive fuzzy feedback controller design problem for finite-time Mittag-Leffler synchronization (FTMLS) of fractional-order quaternion-valued reaction-diffusion T-S fuzzy molecular modeling of delayed neural networks. A novel approach is proposed to effectively deal with the joint effects from fuzzy rules and reaction-diffusion terms for the class of T-S fuzzy fractional-order reaction-diffusion delayed quaternion-valued neural networks (FORDDQVNNs) under consideration. By employing Lyapunov stability theory, Caputo fractional derivative, several algebraic criteria are established to guarantee the FTMLS of T-S fuzzy FORDDQVNNs via designed fuzzy feedback controller. Moreover, the adaptive controller and parameter update laws are designed via adaptive control methods. Compared with existing results in the literature, we also show that our results are less conservative than existing ones with these illustrative T-S fuzzy FORDDQVNNs. A numerical example is presented to verify the analysis results and illustrate the effectiveness of the proposed FTMLS conditions.

We study the issue of finite-time synchronization pertaining to a class of Clifford-valued neural networks with discrete and infinite distributed delays and impulse phenomena. Since multiplication of Clifford numbers is of non-commutativity, we decompose the original n-dimensional Clifford-valued drive and response systems into the equivalent 2 ^m -dimensional real-valued counterparts. We then derive the finite-time synchronization criteria concerning the decomposed real-valued drive and response models through new Lyapunov-Krasovskii functional and suitable controller as well as new computational techniques. We also demonstrate the usefulness of the results through a simulation example.

The issue of adaptive finite-time cluster synchronization corresponding to neutral-type coupled complex-valued neural networks with mixed delays is examined in this research. A neutral-type coupled complex-valued neural network with mixed delays is more general than that of a traditional neural network, since it considers distributed delays, state delays and coupling delays. In this research, a new adaptive control technique is developed to synchronize neutral-type coupled complex-valued neural networks with mixed delays in finite time. To stabilize the resulting closed-loop system, the Lyapunov stability argument is leveraged to infer the necessary requirements on the control factors. The effectiveness of the proposed method is illustrated through simulation studies.

The need for effective heating and cooling systems in the automotive, chemical, and aerospace industries is driving a rapid proliferation of heat-transfer technology. In recent times, GO (Graphene Oxide) has been emerging as one of the most promising nanoparticles because of its uninterrupted behavior of electrical conductivity even at a minimum carrier concentration. Due to this incentive, the behavior of jet flow with heat and mass transfer features of electrically conducting based kerosene oil (KO) fluid dispensed by graphene nanoparticles was studied. In addition, the activation energy, irregular heat source/sink, thermophoretic particle deposition, and chemical reaction are also provoked. In order to provide numerical results, the boundary value problem of fourth-order (bvp4c) solver was used. The graphs were used to illustrate the effects of relevant parameters on the fluid flow, heat, and mass transfer rates. The incorporation of graphene nanoparticles significantly improves heat conductivity. Additionally, the nanoparticle volume fraction augments the temperature and concentration profile while the velocity profile declines. Moreover, the temperature enhances due to the heat source, whilst the contrary behavior is observed in the presence of the heat sink. Furthermore, the shear stress increases up to 12.3%, the Nusselt number increases up to 0.119%, and the Sherwood number increases up to 0.006% due to the presence of nanofluid. Finally, we can conclude that the latest work will be useful for thermal cooling systems, including cooling for engines and generators, nuclear systems, aviation refrigeration systems, and other systems.