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This paper explores the synchronization control issue for a class of fractional-order Complex-valued Neural Networks (FOCVNNs) with additive time-varying delays (TVDs) utilizing a sampled-data-based event-triggered mechanism (SDBETM). First, an innovative free-matrix-based fractional-order integral inequality (FMBFOII) and an improved fractional-order complex-valued integral inequality (FOCVII) are proposed, which are less conservative than the existing classical fractional-order integral inequality (FOII). Secondly, an SDBETM is inducted to conserve network resources. In addition, a novel Lyapunov–Krasovskii functional (LKF) enriched with additional information regarding the fractional-order derivative, additive TVDs, and triggering instants is constructed. Then, through the integration of the innovative FOCVII, LKF, SDBETM, and other analytical methodologies, we deduce two criteria in the form of linear matrix inequalities (LMIs) to ensure the synchronization of the master–slave FOCVNNs. Finally, numerical simulations are illustrated to confirm the validity of the proposed results. [ABSTRACT FROM AUTHOR]

Overf the last few years, by utilizing Mawhin’s continuation theorem of coincidence degree theory and Lyapunov functional, many scholars have been concerned with the global asymptotical stability of positive periodic solutions for the non-linear ecosystems. In the real world, almost periodicity is usually more realistic and more general than periodicity, but there are scarcely any papers concerning the issue of the global asymptotical stability of positive almost periodic solutions of non-linear ecosystems. In this paper we consider a kind of delayed two-species competitive model with stage structure. By means of Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least one positive almost periodic solutions for the above model with nonnegative coefficients. Furthermore, the global asymptotical stability of positive almost periodic solution of the model is also studied. The work of this paper extends and improves some results in recent years. An example and simulations are employed to illustrate the main results of this paper.

This paper addresses the issue of robust stochastic stabilization and H ∞ control of uncertain time-delay Markovian jump quaternion-valued neural networks (MJQVNNs) subject to partially known transition probabilities. First, the direct quaternion method is proposed to analyse the MJQVNNs, which is different from some conventional methods in that the former is without any decomposition for systems. After that, in order to estimate the upper bound of the derivative of the constructed Lyapunov–Krasovskii functional (LKF) more accurately, the real-valued convex inequality is extended to quaternion domain. Then, by designed the mode-dependent state feedback controllers, the robust stochastic stabilization conditions of MJQVNNs are given for the admissible uncertainties, and reduce the influence of input disturbance on the controlled output to a specified performance level. Lastly, two numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Global quadratic stability and L 2 performance in probability (quadratic stability and L 2 gain γ in probability: abbreviated as GQ L 2 (γ) -P) is studied for switched systems consisting of linear stochastic subsystems with norm-bounded uncertainties. Under the assumption that there is no single subsystem achieving GQ L 2 (γ) -P, it is shown that if there exists a convex combination of subsystems achieving GQ L 2 (γ) -P, then a state-dependent switching law, based on the convex combination of subsystems, is proposed under which the switched system achieves GQ L 2 (γ) -P. Then, the discussion is extended to the case involving state feedback controller gain. A numerical example and the application to DC–DC boost converters are provided to demonstrate the proposed design condition and the algorithm. [ABSTRACT FROM AUTHOR]

We propose a class of neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales. Applying the exponential dichotomy of linear dynamic equations on time scales, Banach's fixed point theorem and theory of calculus on time scales, we obtain several sufficient conditions to ensure the existence and global exponential stability of pseudo almost periodic solutions of the proposed neural networks. Finally, we illustrate the effectiveness of the obtained results with an example. The example also shows that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors when considering the pseudo almost periodicity. [ABSTRACT FROM AUTHOR]