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A neural network model upon differential inclusion is designed for solving the complex-variables convex programming, and the chain rule for real-valued function with the complex-variables is established in this paper. The model does not need to choose penalty parameters when applied to practical problems, which makes it easier to design. The result is obtained that its state reaches the feasible region in finite time. Furthermore, the convergence for its state to an optimal solution is proved. Some typical examples are shown for the effectiveness of the designed model., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

In this paper, a class of fractional-order neural networks is investigated. First, α-exponential stability is introduced as a new type of stability and some effective criteria are derived for such kind of stability of the addressed networks by handling a new fractional-order differential inequality. Based on the results, the existence and α-exponential stability of the equilibrium point are considered. Besides, the synchronization of fractional chaotic networks is also proposed. Finally, several examples with numerical simulations are given to show the effectiveness of the obtained results., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

This paper concerns a class of coupled competitive neural networks, subject to disturbance and discontinuous activation functions. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results. [ABSTRACT FROM AUTHOR]

This study aims to unravel the resource allocation problem (RAP) by using a consensus-based distributed optimization algorithm under dynamic event-triggered (DET) strategies. Firstly, based on the multi-agent consensus approach, a novel one-to-all DET strategy is presented to solve the RAP. Secondly, the proposed one-to-all DET strategy is extended to a one-to-one DET strategy, where each agent transmits its state asynchronously to its neighbors. Furthermore, it is proven that the proposed two types of DET strategies do not have Zeno behavior. Finally, numerical simulations are provided to validate and illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the distributed cluster optimisation problem of multi-agent systems (MASs). Different from existing optimisation problems, the MASs are divided into several clusters, and each cluster has its own optimisation objective which is the sum of their local objective functions. Firstly, based on communication topology, the distributed optimisation problem with two clusters is considered and a kind of distributed control protocol is proposed. By using the fixed-time stability theory and the convexity of function, it is proved that the MASs can not only achieve cluster consensus in a fixed-time interval, but also solve the optimisation problem asymptotically. Secondly, the MASs with multiple clusters are further considered. We extend the proposed protocol to a more general case and also prove that MASs can achieve cluster consensus in fixed-time and asymptotically reach the optimal solution of the optimisation objective. Finally, some numerical simulations are presented to show the efficacy of the theoretical results. [ABSTRACT FROM AUTHOR]

The roles of traveling magnetic fields (TMFs) within the transport phenomena during the directional solidification of nickel-based superalloys were simulated. The evolution of thermal field, flow field and solid-liquid interface morphology during the solidification process under both natural and forced convection conditions were also simulated and compared. The strength of TMFs window that suppresses the flow of the interfacial front in the melt was quantified. The association between flow velocity at the interface front and defect formation was discussed. [ABSTRACT FROM AUTHOR]

This paper mainly deals with the issue of fixed-time synchronization of fuzzy-based impulsive complex networks. By developing fixed-time stability of impulsive systems and proposing a T-S fuzzy control strategy with pure power-law form, some simple criteria are acquired to achieve fixed-time synchronization of fuzzy-based impulsive complex networks and the estimation of the synchronized time is given. Ultimately, the presented control scheme and synchronization criteria are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, without dividing complex-variable networks into two subsystems with real values, the finite-time synchronization is considered for complex-valued dynamical networks with fractional order by means of the theory of complex-variable functions. First of all, as a generalization of the real-valued sign function, the sign functions of complex-valued numbers and complex-valued vectors are introduced and some formulas about them are established. Under the sign function framework, two complex-valued control strategies are designed based on two different norms of complex numbers. Some synchronization criteria are derived and the settling times of synchronization are effectively estimated by developing fractional-order finite-time differential inequalities and utilizing the theory of complex-variable functions. The established theoretical results are demonstrated and the effect of the fractional order of the network model on the finite-time synchronization is revealed finally by providing some numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problem of pinning synchronization for delayed complex directed networks via generalized intermittent adaptive control strategy is considered. First, a dynamical mode of delayed network is investigated. Second, a generalized intermittent adaptive control strategy which unified the traditional periodic intermittent control and the aperiodic case is introduced. Additionally, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria to ensure the global synchronization of delayed complex networks based on the designed control protocols are obtained. Finally, an example with numerical simulations is provided to demonstrate the validness of the theoretical results proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, an I2S2R rumor spreading model in complex networks is established and analyzed. Firstly, the threshold value is acquired to identify the existence and stability of rumor-free equilibria state and rumor equilibria state by using the next generation matrix method. Secondly, based on Routh–Hurwitz judgment, Lyapunov stability theory and LaSalle's invariance principle, the local and global stability of rumor-free/rumor equilibrium points are discussed. Thirdly, the sensitivity analysis about the threshold value is given to analyze the impact of model parameters on rumor propagation. Finally, some numerical simulations are presented to illustrate the validity and feasibility of corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, the cluster consensus problem with delays of first-order nonlinear multi-agent systems is studied through pinning leader-following approach with periodic intermittent effect. The graph of the networked system is assumed to be directed and weakly connected. A new type of pinning consensus protocol with intermittent effect is designed according to the ways in which the agents link, specifically, the agents in each cluster are divided into three subsets due to the orientation of their topological degree, and each subset of agents is controlled by an individual law. A redefined notion on cluster consensus with two sorts of time delays is proposed in this article. Some consensus criteria are derived to guarantee that the agents in the same cluster asymptotically follow the virtual leader with a delay, while agents in different clusters reach consensus with delays via following their leaders. Some numerical simulations are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, finite-time synchronization for a class of fuzzy cellular neural networks with time-varying delays is investigated based on the finite-time stability theory. By applying the inequality technique and the analysis method, some new and useful criteria of finite-time synchronization for the addressed network are derived in terms of p -norm. Finally, two examples with their numerical simulations are given to show the feasibility and effectiveness of the developed synchronization method. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of global and local finite-time synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying delays by designing an appropriate feedback controller. Through a nonlinear transformation, we derive an alternative system from the considered memristor-based Cohen–Grossberg neural networks. Then, by considering the finite-time synchronization of the alternative system, we obtain some novel and effective finite-time synchronization criteria for the considered memristor-based Cohen–Grossberg neural networks. These results generalize and extend some previous known works on conventional Cohen–Grossberg neural networks. Finally, numerical simulations are given to present the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the exponential synchronization for a class of complex networks with finite distributed delays coupling is studied via periodically intermittent control. Some novel and useful criteria are derived by utilizing a different technique compared with some correspondingly previous results. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural networks with distributed delays are obtained. Furthermore, a feasible region of the control parameters is derived for the realization of exponential synchronization. It is worth noting that the synchronized state in this paper is not an isolated node but a non-decoupled state, in which the inner coupling matrix and the degree of the nodes play a central role. Additionally, the traditional assumptions on control width, non-control width, and discrete delays are removed in our results. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed control method. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we mainly study the distribution of the roots of a fifth degree exponential polynomial. We obtain the sufficient and necessary conditions for the existence of purely imaginary roots of the exponential polynomial. Applying the obtained results, we consider a neural network model consisting of five neurons with delays. The sum of delays is regarded as the bifurcation parameter. Under some conditions, we show that the zero solution is locally asymptotically stable when the time delay is suitably small, while change of stability of zero solution will cause a bifurcating periodic solution as the time delay passes through a certain critical value. In order to illustrate our theoretical analysis, some numerical simulations are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate bidirectional associative memory Cohen–Grossberg neural networks with time delays. By applying the Young inequality technique, Dini derivative, and introducing many real parameters, a series of new and useful criteria on the existence and uniqueness of an equilibrium point and its global asymptotical stability are established. It is shown that in some special cases of the results, the stability criteria can be easily checked. Finally, an example is given to illustrate the result obtained in this paper. [Copyright &y& Elsevier]

A continuous-time distributed algorithm based on multi-agent systems is proposed to solve the convex nonsmooth optimization with globally coupled constraints in this paper. Firstly, the relationship of equivalence between the equilibrium and the optimal solution of the system is proved by using the properties of projection operator and saddle point. In addition, the stability of the algorithm is analyzed by means of Lie derivative and set-valued LaSalle's invariance principle. In particular, the trajectory of the proposed algorithm from any initial point can converge to the global optimal solution. Finally, the effectiveness of the designed algorithm is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

The actuator of any physical control systems is constrained by amplitude and energy, which causes the control systems to be inevitably affected by actuator saturation. In this paper, impulsive synchronization of coupled delayed neural networks with actuator saturation is presented. A new controller is designed to introduce actuator saturation term into impulsive controller. Based on sector nonlinearity model approach, impulsive controls with actuator saturation and with partial actuator saturation are studied, respectively, and some effective sufficient conditions are obtained. Numerical simulation is presented to verify the validity of the theoretical analysis results. Finally, the impulsive synchronization is applied to image encryption. The experimental results show that the proposed image encryption system has high security properties. [ABSTRACT FROM AUTHOR]

This paper is concerned with the issue of fixed-time (FT) and preassigned-time (PT) synchronization of impulsive complex networks (ICNs) with mismatched parameters. Firstly, several more succinct conditions are established to achieve FT stability of impulsive systems and an improved estimation for the stable time is given. Subsequently, based on the improved FT stability results, the FT synchronization criteria for ICNs with mismatched parameters are proposed by designing fixed-time controllers without the linear part. Correspondingly, the PT synchronization problem is also considered by developing several innovative control protocols, where the synchronized time can be arbitrary predefined according to task demands and the control gains are bounded. Ultimately, the presented synchronization criteria are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the stabilization for a class of nonlinear systems with time-varying delays is proposed via impulsive control. Using some analysis techniques such as reduction to absurdity, some new and useful criteria for global exponential stability are established. Furthermore, an example and some numerical simulations are presented to verify the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper, the global projective synchronization of fractional-order neural networks is investigated. First, a sufficient condition in the sense of Caputo’s fractional derivation to ensure the monotonicity of the continuous and differential functions and a new fractional-order differential inequality are derived, which play central roles in the investigation of the fractional adaptive control. Based on the preparation and some analysis techniques, some novel criteria are obtained to realize projective synchronization of fractional-order neural networks via combining open loop control and adaptive control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the addressed neural networks. Finally, an example with numerical simulations is given to show the effectiveness of the obtained results. [Copyright &y& Elsevier]

Abstract: In this paper, a class of fractional-order neural networks is investigated. First, -exponential stability is introduced as a new type of stability and some effective criteria are derived for such kind of stability of the addressed networks by handling a new fractional-order differential inequality. Based on the results, the existence and -exponential stability of the equilibrium point are considered. Besides, the synchronization of fractional chaotic networks is also proposed. Finally, several examples with numerical simulations are given to show the effectiveness of the obtained results. [Copyright &y& Elsevier]

Abstract: In this paper, the dynamical behaviors of a class of discrete-time SIRS epidemic models are discussed. The conditions for the existence and local stability of the disease-free equilibrium and endemic equilibrium are obtained. The numerical simulations not only illustrate the validity of our results, but also exhibit more complex dynamical behaviors, such as flip bifurcation, Hopf bifurcation and chaos phenomenon. These results reveal far richer dynamical behaviors of the discrete epidemic model compared with the continuous epidemic models. [Copyright &y& Elsevier]

Abstract: In this Letter, the complex dynamical networks with community structure and nonidentical nodes are considered. The globally asymptotical synchronization of the time-delayed complex community networks onto any uniformly smooth state is studied. Some simple and useful criteria are derived by constructing an effective control scheme and adjusting automatically the adaptive coupling strength. Finally, the developed techniques are applied to two complex community networks which are respectively synchronized to a chaotic trajectory and a periodic orbit, and numerical simulations are provided to show the feasibility of the developed methods. [ABSTRACT FROM AUTHOR]

In this paper, the problem of synchronization for a class of fractional-order delayed spatio-temporal neural networks with Dirichlet boundary conditions is investigated. Firstly, based on the L'Hopital law, a Caputo fractional partial differential inequality with p -norm is established to improve the previous results. Besides, a generalized fractional-order Halanay inequality is introduced by rigorous theoretical deduction. Additionally, to realize synchronization, two different control schemes are designed for the networks, respectively, and several criteria are derived based on the developed fractional inequalities. Finally, numerical examples and simulations are provided to verify the correctness of the results. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time synchronization and parameter identification (FTSPI) problem of uncertain fractional-order complex dynamical networks. By utilizing the properties of fractional calculus and some analysis techniques, several sufficient conditions are given to guarantee FTSPI via designing suitable controller and parameter update law. In addition, the estimation bound of the setting time is also given. Finally, numerical simulations are provided to illustrate the effectiveness of our obtained theoretical results. • The novel controller and parameter identification law are designed. • Several simple FTSPI criteria are obtained. • The estimation bound of the setting time is explicitly evaluated. [ABSTRACT FROM AUTHOR]

In this paper, without separating the complex-valued neural networks into two real-valued systems, the quasi-projective synchronization of fractional-order complex-valued neural networks is investigated. First, two new fractional-order inequalities are established by using the theory of complex functions, Laplace transform and Mittag-Leffler functions, which generalize traditional inequalities with the first-order derivative in the real domain. Additionally, different from hybrid control schemes given in the previous work concerning the projective synchronization, a simple and linear control strategy is designed in this paper and several criteria are derived to ensure quasi-projective synchronization of the complex-valued neural networks with fractional-order based on the established fractional-order inequalities and the theory of complex functions. Moreover, the error bounds of quasi-projective synchronization are estimated. Especially, some conditions are also presented for the Mittag-Leffler synchronization of the addressed neural networks. Finally, some numerical examples with simulations are provided to show the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]