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An Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R 0 is obtained by the next generation matrix method to ensure the existence of rumor-prevailing equilibrium. Secondly, by utilizing the Routh–Hurwitz criterion and LaSalle's invariance principle, the local stability and global stability of rumor equilibria are proved. Moreover, the optimal control is presented via Pontryagin's minimum principle, which is to effectively restrain rumor diffusion. Finally, the theoretical results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization of fractional-order competitive neural networks with reaction–diffusion terms and time delays. A novel method that combines the fractional-order Lyapunov theorem with M-matrix theory is utilized to cope with synchronization for the addressed networks. Based on such approach and developing two different controllers, some sufficient criteria are derived to guarantee global synchronization by employing the properties about Mittag–Leffler and trigonometric functions, comparison principle as well as the method of contradiction. Finally, a numerical example is provided to show the effectiveness of the established result. [ABSTRACT FROM AUTHOR]

In this paper, a periodic intermittent sampled data control strategy, which both reduces the load of updating rate of the controller and cuts down the working time of the controller in each sampling interval, is proposed to investigate the second-order consensus of multiagent systems. In order to reach consensus, a necessary and sufficient condition depending on the coupling gains, the communication width, the sampling period, and the spectrum of the Laplacian matrix, is established. Furthermore, the feasible region of communication width is derived for given coupling gains and structure of network. Besides, the coupling gains are also carefully designed. On the other hand, when the time delay exists in the sampling process, a time delayed protocol is proposed. A necessary and sufficient condition based on the communication width, the sampling period, the coupling gains, the time delay, and the network structure is also derived for achieving consensus. It is amazing found that the sampling period should have both lower and upper bounds for given time delay and communication width for the sake of reaching consensus. Finally, several numerical simulations are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the finite-time synchronization (FTS) is studied for a class of delay neural networks (DNNs) via aperiodically intermittent control. Based on the finite-time stability theory, several new conditions ensuring FTS of two DNNs are derived by establishing a very useful differential inequality and constructing a new Lyapunov function. In addition, the proposed results here are easy to verify and they also extend the previous publications. And, the upper bounds of the settling time for synchronization are estimated. Finally, numerical simulations show the effectiveness of the derived results and the developed method. [ABSTRACT FROM AUTHOR]

This paper considers the delay-dependent stability of memristive complex-valued neural networks (MCVNNs). A novel linear mapping function is presented to transform the complex-valued system into the real-valued system. Under such mapping function, both continuous-time and discrete-time MCVNNs are analyzed in this paper. Firstly, when activation functions are continuous but not Lipschitz continuous, an extended matrix inequality is proved to ensure the stability of continuous-time MCVNNs. Furthermore, if activation functions are discontinuous, a discontinuous adaptive controller is designed to acquire its stability by applying Lyapunov–Krasovskii functionals. Secondly, compared with techniques in continuous-time MCVNNs, the Halanay-type inequality and comparison principle are firstly used to exploit the dynamical behaviors of discrete-time MCVNNs. Finally, the effectiveness of theoretical results is illustrated through numerical examples. [ABSTRACT FROM AUTHOR]

The global stability problem for a class of complex-valued neural networks with both mixed time delays and impulsive effect is concerned in this literature. By using Schur complement, forming an equivalent matrix, and constructing an appropriate Lyapunov functional, some new sufficient criteria to ascertain the existence, uniqueness, globally exponential stability and globally asymptotical stability of the equilibrium point of complex-valued neural networks are obtained in terms of linear matrix inequality techniques. Meanwhile, several linear matrix inequalities have been proved in the literature, which shall be used to prove the stability of the equilibrium point. Finally, simulation results of one numerical example are also delineated to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization of a class of improved neural networks with variable time delay is concerned via intermittent control. Firstly, a class of modified delayed neural networks is introduced, in which communication delays between different neurons are considered and the intra-neuron delays are negligible. Secondly, using Lyapunov functional theory, inequality techniques, and multi-parameter method, the synchronization criteria are established based on p-norm via intermittent control, and a feasible synchronization control region is given. Besides, by means of the component analysis method, the reduction to absurdity, mathematical induction, the exponential synchronization of the addressed networks is discussed in terms of the infinite norm, some criteria and the feasible control region of synchronization are also derived. Finally, some numerical examples are provided to show the validity and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates a new type of stability, namely global generalized exponential stability of the nonautonomous delayed cellular neural networks. Several novel delay-dependent sufficient conditions are established by applying a new generalized Halanay inequality. In these conditions, the boundedness of time-varying delays and coefficients are not required. In addition, the effectiveness of these conditions is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor, which is an ideal tool to mimic the functionalities of the human brain. In this paper, finite-time synchronization is considered for a class of memristor-based neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of memristor-based chaotic neural networks are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the exponential synchronization for a class of delayed recurrent neural networks is investigated by virtue of intermittent control schemes. Based on p-norm and , respectively, several new and useful synchronization criteria are derived by applying Lyapunov functional theory, mathematical induction and inequality technique. Particularly, some feasible regions of control parameters for each neuron are derived for the realization of exponential synchronization, which provides great convenience to the applications of the theoretical results. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed control methods. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with a model of single genetic negative feedback autoregulatory system with delay. Choosing the transcriptional rate k as the bifurcation parameter, we demonstrate that the Hopf bifurcation would occur when k exceeds a critical value. By using the normal form theory and center manifold argument, we derive the explicit formulas which determine the bifurcation direction and the stability of bifurcated periodic solution. In order to illustrate our theoretical analysis, a numerical simulation is also included in the end. [Copyright &y& Elsevier]

This paper investigates the exponential stability for a class of mixed delayed genetic regulatory networks by periodically intermittent control, mixed delays here include time-varying delays and finite distributed delays. Some sufficient criteria for exponential stabilization are derived by using mathematical induction methods and the analysis techniques. Finally, an example is presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a time-delayed impulsive controller is constructed and the uniformly asymptotic stability of chaotic systems based on a Takagi–Sugeno (TS) fuzzy model is investigated and some new and useful criteria are derived. In addition, the uniformly asymptotic synchronization of chaotic systems based on the TS fuzzy model is discussed using similar techniques. Finally, some numerical simulations are presented to illustrate the effectiveness and feasibility of the derived results. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate robust stochastic stability of Markovian switching genetic regulatory networks with discrete and distributed delays. Different from previous correspondingly works, discrete and distributed delays are involved to describe the concentration of macromolecule for genetic networks. Based on the Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions are given to ensure the stability in the mean square of the stochastic genetic networks with Markovian switching. An illustrative example is given to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the uniformly boundedness and uniformly ultimately boundedness of high-order neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are uniformly bounded and uniformly ultimately bounded. The results are shown to improve the results derived in (Arik, 2004). Some examples are given to illustrate the correctness of our results. [ABSTRACT FROM AUTHOR]

Abstract: By using the continuation theorem of coincidence degree theory and constructing a suitable Lyapunov functional, we derive some sufficient conditions for the existence and global exponential stability of a unique periodic solution of BAM neural networks, which assumes neither the monotony nor the boundedness of the activation functions. It is believed that these results are significant and useful for the design and applications of BAM neural networks. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the cellular neural networks with variable coefficients and infinite distributed delays. By introducing the phase space and applying Lyapunov functional method and Young inequality technique, we first establish a series of criteria on the boundedness, globally asymptotic stability and globally exponential stability. Furthermore, by applying these results and combining the existence theorems of periodic solutions for general functional differential equations with infinite delays, we establish the existence of periodic solutions and its globally asymptotic stability and globally exponential stability for the periodic cellular neural networks with infinite distributed delays. At last, as a special case, we apply these results to the autonomous cellular neural networks with infinite distributed delays and the existence, uniqueness and global stability of equilibrium point are established. [Copyright &y& Elsevier]

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: The purpose of this manuscript is to study the dynamics of a damped harmonic oscillator with delayed feedback. Different to previous papers, the bifurcation when the linearization at an equilibrium has, for critical value of the parameters, a pair of non-semisimple purely imaginary eigenvalues with geometric multiplicity one and algebraic multiplicity two is considered. By employing the Lyapunov–Schmidt reduction, the criteria for the existence and number of branches of bifurcating periodic solutions are derived. Finally, some numerical simulations are given to support the analytic results. [Copyright &y& Elsevier]

Abstract: In this paper, the globally exponential synchronization for a class of reaction–diffusion neural networks with Dirichlet boundary conditions and mixed delays is investigated based on periodically intermittent control. Some new and useful synchronization criteria in terms of -norm are derived by introducing multi-parameters, using Lyapunov functional theory. Subsequently, a feasible region of the control parameters for each neuron is derived for the realization of exponential synchronization. Besides, according to the theoretical results, the influences of diffusion strengths and diffusion spaces on synchronization are analyzed and a very interesting fact is revealed that the synchronization of neural networks with reaction–diffusions is more easily realized than those of neural networks without reaction–diffusions. Finally, a reaction–diffusion chaotic network is given to demonstrate the effectiveness of the proposed control methods. [Copyright &y& Elsevier]

Abstract: In this paper, a class of Cohen–Grossberg neural networks with time-varying delays are studied by designing a periodically intermittent controller. Some novel and effective exponential synchronization criteria are derived by applying some analysis techniques. These results generalize a few previous known results and remove some restrictions on control width and time-delays. Finally, a chaotic Cohen–Grossberg neural network is represented to show the effectiveness and feasibility of our results. [Copyright &y& Elsevier]

This paper studies quasi-projective synchronization (QPS) and complete synchronization (CS) for a class of fractional-order complex-valued neural networks with time delays by designing suitable controllers. To realize QPS and CS, linear feedback controller and adaptive controller are designed, and a novel fractional-order differential inequality is built by means of Laplace transform and properties of Mittag-Leffler function. By utilizing Lyapunov method, our proposed inequality, fractional-order Razumikhin theorem and some complex analysis techniques, some effective criteria are derived to ensure QPS and CS of the considered networks. Furthermore, the error bound of QPS is obtained. Finally, some numerical results are given to demonstrate the effectiveness of the presented theoretical results. [ABSTRACT FROM AUTHOR]

• Based on quaternion theory, Mittag-Leffler function and nabla h -Laplace transform, two new inequalities are obtained. • In order to realize synchronization more conveniently, we design a quaternion controller with time delay. • Under the direct quaternion framework, quasi-synchronization criteria of DTFQMNNs are obtained by utilizing our lemmas and some analysis techniques. Besides, the error bound for quasi-synchronization is evaluated. In this paper, quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks (DTFQMNNs) with time delays and uncertain parameters is investigated. Firstly, some related preliminaries are introduced and two new inequalities are obtained based on nabla fractional difference, quaternion theory and nabla h -Laplace transform. Then, a quaternion-valued controller with time delay is designed to realize quasi-synchronization goal, and some sufficient criteria are derived to guarantee quasi-synchronization of DTFQMNNs by using our created inequalities and some analysis techniques. Finally, a numerical example is provided to verify the correctness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: A four-dimension genetic regulatory network model with double genes and four delays is considered. The existence of Hopf bifurcation is first considered and then explicit formulas are derived by using the normal form method and center manifold theory to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Finally, numerical simulations are carried out to support the theoretical analysis of the research. [ABSTRACT FROM AUTHOR]