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.

The discrete‐time system has more complex and chaotic dynamical behaviors as compared to the continuous‐time system. This paper extends a discrete Leslie–Gower predator‐prey system with the Allee effect in the predator’s population, whose dynamics are analyzed and explored. We have determined the equilibrium points and studied their local stability properties. We find that the system undergoes flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point by choosing the Allee parameter as a bifurcation parameter. We discuss the stability and direction of both bifurcations with the help of the normal form theory and center manifold theorem. The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. The work is complete with the numerical simulations to confirm the analytical findings.

In this paper, we focus on the global stability analysis with respect to dynamical delayed neural network (NN) models 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 NN models have been conducted. In this study, a new upper bound of the norm of connection weight matrices is derived for the delayed NN models 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 NN models. The slope bounded activation functions and Lyapunov-Krasovskii functionals are employed for formulating the sufficient conditions of the NN equilibrium point. 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.

In this paper, we study the Hyers-Ulam stability with respect to the linear differential condition of fourth order. Specifically, we treat ${\psi}$ as an interact arrangement of the differential condition, i.e., $ \begin{align*} {\psi}^{iv} ({\varkappa}) + {\xi}_1 {\psi}{'''} ({\varkappa})+ {\xi}_2 {\psi}{''} ({\varkappa}) + {\xi}_3 {\psi}' ({\varkappa}) + {\xi}_4 {\psi}({\varkappa}) = {\Psi}({\varkappa}) \end{align*} $ where ${\psi} \in c^4 [{\ell}, {\mu}], {\Psi} \in [{\ell}, {\mu}]$. We demonstrate that ${\psi}^{iv} ({\varkappa}) + {\xi}_1 {\psi}{'''} ({\varkappa})+ {\xi}_2 {\psi}{''} ({\varkappa}) + {\xi}_3 {\psi}' ({\varkappa}) + {\xi}_4 {\psi}({\varkappa}) = {\Psi}({\varkappa})$ has the Hyers-Ulam stability. Two examples are provided to illustrate the usefulness of the proposed method.