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In this paper, we analyze the global asymptotic stability and global exponential stability with respect to the Clifford-valued neutral-type neural network (NN) models with time delays. By considering the neutral term, a Clifford-valued NN model with time delays is formulated, which encompasses real-valued, complex-valued, and quaternion-valued NN models as special cases. In order to achieve our main results, the n -dimensional Clifford-valued NN model is decomposed into 2 m n -dimensional real-valued models. Moreover, a proper function is constructed to handle the neutral term and prove that the equilibrium point exists. Utilizing the homeomorphism theory, linear matrix inequality as well as Lyapunov functional methods, we derive the sufficient conditions corresponding to the existence, uniqueness, and global asymptotic stability with respect to the equilibrium point of the Clifford-valued neutral-type NN model. Numerical examples to demonstrate the effectiveness of the results are provided, and the simulations results are analyzed and discussed.

An m - Ł ℘ , ℘ − 1 , … , 1 labeling of a simple graph G is a mapping τ from the vertex set ∨ G to 0,1 , … , m such that τ u − τ v ≥ ℘ + 1 − d u , v , ∀ u , v ∈ ∨ G , where length of the shortest route connecting u and v is represented by d u , v . The smallest m for which there exists a m - Ł ℘ , ℘ − 1 , … , 1 labeling of G is known as the Ł ℘ , ℘ − 1 , … , 1 labeling number of G , and it is described by λ ℘ G . We define m - Ł ′ ℘ , ℘ − 1 , … , 1 as the same as the m - Ł ℘ , ℘ − 1 , … , 1 labeling if τ is one to one. The Ł ′ ℘ , ℘ − 1 , … , 1 labeling number of G represented by λ ℘ , ℘ − 1 , … , 1 ′ G and is called minimum span. In this paper, we prove that the circulant graphs with specified generating sets admit m - Ł ℘ , ℘ − 1 , … , 1 and m - Ł ′ ℘ , ℘ − 1 , … , 1 labeling and also find λ ℘ G and λ ℘ , ℘ − 1 , … , 1 ′ G . Moreover, we find the Ł ℘ , ℘ − 1 , … , 1 labeling number of any simple graph with diameter less than ℘ .

In this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account from both biological and mathematical points of view. We explore the influence of the Allee and fear effect on the existence of all positive equilibria. Furthermore, the local stability properties and possible bifurcation behaviors of the proposed system about positive equilibria are discussed with the help of trace and determinant values of the Jacobian matrix. With the help of Sotomayor’s theorem, the conditions for existence of saddle-node bifurcation are derived. Also, we show that the proposed system admits limit cycle dynamics, and its stability is discussed with the value of first Lyapunov coefficient. Moreover, the numerical simulations including phase portrait, one- and two-parameter bifurcation diagrams are performed to validate our important findings.

This work investigates the finite-time event-triggered approach for recurrent neural networks with leakage term and its application. Here, decentralized event-triggered framework is recommended where event is checked at every sensor node related to local information for available triggering and the updated control is done whenever a centralized event is triggered. By handling the Lyapunov–Krasovskii functional (LKF) method together with novel inequality techniques like Wirtinger single and double integral inequality (WSI,WDI) technique, delay productive term (DPT), and a few adequate conditions are acquired to ensure the finite-time stability (FTS) analysis for the considered system, which is expressed with respect to linear matrix inequalities (LMIs). At last, numerical simulations are provided to indicate the efficiency of the expected results, two of these examples were supported by genuine use of the benchmark issue that correlates with sensible concerns under finite-time execution.

This study is concerned about the stabilization for delayed fuzzy neutral-type system (DFNTS) with uncertain parameters under intermittent control. Firstly, by constructing the augmented Lyapunov-Krasovskii functional (LKF) about different time delays along with single and double auxillary function-based integral inequalities (SAFBII, and DAFBII, respectively), a new class of delay-dependent adequate conditions are proposed, so that the robust fuzzy neutral-type system under consideration is guaranteed to be globally asymptotically stable (GAS). Secondly, the intermittent control (IC) is introduced to stabilize the system with mixed time-varying delays. In the view of inferred adequate conditions, the IC parameters are determined as for the arrangement of linear matrix inequalities (LMIs). It is noted that the strategies exploited in this work are apart from the other methods engaged in the literature, and the proposed conditions are less conservative. Finally, numerical examples are given to demonstrate the effectiveness of the developed techniques in this work. One of the practical applications is single-link robot arm (SLRA) model to show the viability and benefits of the structured intermittent control.

This article examines the issue of event-triggered $L_{2}-L_\infty $ filtering for network-based neutral systems via Takagi-Sugeno (T-S) fuzzy approach. A dynamic discrete event-triggered scheme (ETS) is introduced to save the limited communication resource. Based on the T-S fuzzy model, the consider neutral type system with networked induced delays are represented as a class of T-S fuzzy system. In addition, by considering a suitable Lyapunov-Krasovskii functional (LKF) and by using the Wirtinger inequality technique, the stability conditions with respect to linear matrix inequalities (LMIs) are presented to guarantee the considered filtering systems are asymptotically stable with $L_{2}-L_{\infty }$ performance index $\gamma $ . To the end, numerical examples are given to illustrate the effectiveness of the proposed result.

In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.

This article examines the issue of event-triggered $L_{2}-L_\infty $ filtering for network-based neutral systems via Takagi-Sugeno (T-S) fuzzy approach. A dynamic discrete event-triggered scheme (ETS) is introduced to save the limited communication resource. Based on the T-S fuzzy model, the consider neutral type system with networked induced delays are represented as a class of T-S fuzzy system. In addition, by considering a suitable Lyapunov-Krasovskii functional (LKF) and by using the Wirtinger inequality technique, the stability conditions with respect to linear matrix inequalities (LMIs) are presented to guarantee the considered filtering systems are asymptotically stable with $L_{2}-L_{\infty }$ performance index $\gamma $ . To the end, numerical examples are given to illustrate the effectiveness of the proposed result.

In this paper, we focus on the global stability analysis with respect to dynamical delayed neural networks (NNs) that contain parameter uncertainties. Many investigations on the sufficient conditions utilizing different upper bounds for the norm of interconnection matrices pertaining to the global asymptotic robust stability of delayed NNs have been conducted. In this study, a new upper bound of the norm of connection weight matrices is derived for the delayed NNs under parameter uncertainties. The key focus is on how the new upper bound is able to yield minimum result with respects to some of the existing upper bounds. We demonstrate that the new upper bound can lead to some new sufficient conditions with respect to the global asymptotic robust stability of equilibrium point of the delayed NNs. The slope bounded activation functions and Lyapunov-Krasovskii functionals (LKFs) are employed for formulating the sufficient conditions of the equilibrium point of NNs. Moreover, the derived sufficient conditions are independent on the time delay parameter. Numerical examples are provided and the outcomes obtained are compared with those of the existing results subject to different network parameters.

This research mainly focuses on the effects of heat absorption/generation and radiation on the hydromagnetic flow of Fe3O4-ethylene glycol nanofluid through a shrinking wall with porous medium and the computation of the entropy generation. We considered basic governing ordinary differential equations into partial differential equations by using appropriate similarity solutions. Moreover, hyper geometric function is employing to determine the formulated problem. We analyze the effects of appropriate physical parameters on the Bejan number, Entropy generation, Nussult number, skin friction, fluid temperature and velocity profiles. In addition, the derived result of the present study is compared with those in the existing literature. We noted that the presence of heat absorption and suction parameters reduces the Bejan number and increases the entropy generation, and the heat source, porous medium, radiation parameters minimize the entropy production. The presence of porosity parameter reduced the fluid velocity, improved fluid temperature and minimized the entopy production. Nanosolid volume fraction parameter reduced both Nussult number and skin friction coefficient.

In the current study, we conduct an investigation into the Hyers–Ulam stability of linear fractional differential equation using the Riemann–Liouville derivatives based on fractional Fourier transform. In addition, some new results on stability conditions with respect to delay differential equation of fractional order are obtained. We establish the Hyers–Ulam–Rassias stability results as well as examine their existence and uniqueness of solutions pertaining to nonlinear problems. We provide examples that indicate the usefulness of the results presented.

Impact of non-uniform heat source/sink and elastic deformation on entropy generation analysis for Cu − Fe3O4/ethylene glycol hybrid nanofluid flow past a stretching sheet with an inclined magnetic field, partial slip, and thermal radiations are investigated. Appropriate conversions are utilized for PDE's into ODE's. The dimensionless form is then analytically solved with the help of a hypergeometric function. Performance of significant variables on the hybrid nanofluid flow, heat distribution, skin friction coefficient, Nusselt number, and entropy generation are obtained and discussed with the help of different graphs. Some main results reported in this article reveals that the presents of hybrid nanoparticle, partial slip, inclined magnetic field, and Eckert number improve the more heat conduction in Cu − Fe3O4/ethylene glycol hybrid nanofluid and Partial slip, non-uniform heat source, and Eckert numbers are minimized the entropy production. Skin friction coefficient improves through higher values of Cupper nanoparticles and suction parameter. Heat transfer rate is more for higher values of Cupper nanoparticles, non-uniform heat source, partial slip, thermal radiation, and Eckert number.

This paper deals with the global asymptotic robust stability (GARS) of neural networks (NNs) with constant time delay via Frobenius norm. The Frobenius norm result has been utilized to find a new sufficient condition for the existence, uniqueness, and GARS of equilibrium point of the NNs. Some suitable Lyapunov functional and the slope bounded functions have been employed to find the new sufficient condition for GARS of NNs. Finally, we give some comparative study of numerical examples for explaining the advantageous of the proposed result along with the existing GARS results in terms of network parameters.