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In this paper, we explore complete synchronization for the delayed discrete-time fractional-order competitive neural networks (DDFCNNs). Firstly, several definitions with respect to Caputo fractional-order difference are given. Next, a novel method for proving Caputo fractional difference inequality of 2 k -norm function is given, then by making use of the inequality we prove and Hanalay inequality, some sufficient criteria on complete synchronization of DDFCNNs are obtained under the linear feedback controller. In the end, some numerical simulations are given to verify effectiveness of the theoretical consequences. • A novel approach is put forward to prove discrete-time Caputo fractional inequality on 2 k -norm function based on some definitions and lemmas of fractional difference. • To achieve complete synchronization of DDFCNNs, we design a brief linear feedback controller, which is easier than adaptive controller designed in [34]. • Several sufficient conditions on complete synchronization of DDFCNNs are attained by our established lemma. [ABSTRACT FROM AUTHOR]

The motivation of this paper is inspired by the research of Zanette et al. (2011) [4] , which reveals that the perception of predation risk can reduce the number of juvenile prey. To investigate how fear affects the behavior of prey population, we formulate a predator-prey model with a stage structure for prey in which adult prey is undergoing the interference of fear. First, the dynamic properties of the model are analyzed, including the existence and stability of equilibria, bifurcations dynamics, such as transcritical, saddle-node, and Hopf bifurcations. Our results reveal that fear can promote the formation of the stability of the model by transforming it from an unstable state to a stable state. Numerical simulations and theoretical analysis indicated that when the level of fear reaches 25.4, the number of juvenile prey affected by fear decreases by 40% compared to those not affected by fear. Terrifyingly, the predators are on the brink of extinction in high levels of fear. Moreover, we examine the impact of time delay on fear in the previous model as prey needs some time to assess the predation risk. Some dynamic characteristics of this delayed model are also analyzed. Results indicate that the fear effect is conducive to generating a stable state, while delay is detrimental to generating a stable state, leading to limit cycles or even chaos. • A stage-structure predator-prey model with fear and delay is proposed. • The feasibility equilibria and bifurcation dynamics of the model are studied. • Fear can transform a model from an unstable state to a stable state. • Delay is detrimental to generating a stable state, leading to limit cycles or chaos. [ABSTRACT FROM AUTHOR]

This paper investigates practical stabilization of multi-links highly nonlinear Takagi-Sugeno fuzzy complex networks with Lévy noise (MHFNLs) via aperiodically intermittent discrete-time observation control (AIDOC). It is worth pointing out that AIDOC is considered into MHFNLs for the first time. Due to the difficulty of satisfying linear conditions in real life, polynomial growth conditions are used instead of linear growth conditions. Meanwhile, a global Lyapunov function is constructed and sufficient conditions which can remain MHFNLs practically stable are gained. Finally, an application and its numerical simulations are presented to verify the effectiveness and availability of the theoretical results. • Polynomial growth conditions are used instead of linear growth conditions. • We consider Lévy noise and construct a global Lyapunov function. • Aperiodically intermittent discrete-time observation control is designed. • The theoretical result is applied to Van der Pol-Duffing oscillator. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the cooperative robust consensus tracking problem of uncertain networked Euler-Lagrange systems (NELSs) with time-varying delays and output constraints. By systematically integrating the neural network (NN) adaptive technique and the logarithmic type Barrier Lyapunov Function (BLF) in combination with the additional robust control law, two distributed robust consensus schemes for uncertain NELSs are proposed for two cases of time-varying communication and input delays respectively, which can fully guarantee to constrain the output consensus error within a safety region simultaneously. Furthermore, numerical simulation examples are provided to demonstrate the comparable potential advantages of the proposed robust control law over some existing algorithms, including adaptability, stability, and robustness, as well as delay effects. • An NN-based robust controller is designed to effectively handle the uncertainty of NELSs. • Combining NN with BLF ensures the adaptability, stability, and robustness of the consensus tracking scheme for NELSs. • A unified analytical framework is developed by deriving upper bounds on the allowed values of communication and input delays. [ABSTRACT FROM AUTHOR]

The backward substitution method is a newly developed meshless method that has been used for the simulation of many problems in science and engineering with high accuracy and efficiency. In this paper, we explore the feasibility of employing the backward substitution method for simulating two-dimensional incompressible flows. Two non-increment pressure correction projection methods are considered to decompose the original velocity and pressure coupling system into two boundary value problems of intermediate velocity and pressure. Then, two boundary value problems are solved by the backward substitution method in each time iteration step. Five numerical examples are provided to demonstrate the accuracy, computational efficiency and convergence of the method. Comparisons with some existing meshless methods verify the method's advantages and potential applications to engineering. • The backward substitution method is first raised for the simulation of incompressible flows. • Investigated effects of the time step and the number of collocation points on the accuracy. • Verification benchmark comprising several fluid flows problems. • Two projection methods are considered to verify the algorithm. • The algorithm is easily extended to three-dimensional incompressible flows. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the consensus problem of leaderless multi-agent systems with external disturbance under denial-of-service (DoS) attacks. First, the state predictor is constructed to reproduce the state information blocked during the active periods of DoS attacks. Then, a robust non-smooth consensus protocol is designed using the predictor states, which mitigates the open-loop phenomenon caused by the DoS attacks. Besides, we obtain the sufficient condition for agents to achieve consensus within a region, and demonstrate that the protocol can enhance the anti-disturbance and anti-attack capabilities of the systems. Finally, the theoretical results are verified through numerical simulations. • We introduce a non-smooth consensus protocol based on predictive data to enhance the resilience of multi-agent systems against attacks. The incorporation of distributed predictors prevents the system from entering an open-loop mode due to data unavailability during active periods of DoS attacks. This ensures the avoidance of severe uncontrolled divergence behaviors of multi-agent systems during active periods of attack, thus ensuring rapid consensus recovery as the dormant periods of DoS attack start. • As observed in the current research on multi-agent system control under DoS attacks, linear or sliding mode consensus algorithms are commonly employed. In this study, by incorporating non-smooth functions, the multi-agent system is endowed with faster convergence speed and stronger disturbance resistance capacity. • We incorporate the multiple inertially stabilized platforms system. The effectiveness and superiority of the proposed consensus protocol are demonstrated through comparison with traditional consensus protocols. This not only offers empirical substantiation for future investigations but also emphasizes the practical applicability of studying the consensus of first-order multi-agent systems with external disturbance under DoS attacks. [ABSTRACT FROM AUTHOR]