Search

This paper mainly investigates the problem of the exponential synchronisation for delayed neutral-type multi-weights complex networks (DNMCNs) with regime-switching jump diffusion under aperiodically intermittent control. Compared with the related works, hybrid time delays and regime-switching jump diffusion are introduced into neutral-type networks which can better simulate more complicated practical applications. The introduction of regime-switching jump diffusion increases the difficulties of synchronisation analysis in comparison with the Markovian jump diffusion. Meanwhile, it is noteworthy that we firstly extend the availability of aperiodically intermittent control scheme to handle the synchronisation issue with DNMCNs. On the basis of a technique that combines the Lyapunov method and graph theory, some sufficient criteria to synchronise DNMCNs via intermittent control are obtained. Finally, an oscillator system is considered as the application, and the corresponding numerical simulations are proposed to validate the applicability of the obtained theorems and show the effectiveness. [ABSTRACT FROM AUTHOR]

In previous work, the synchronization of multi-links systems with Lévy noise (MLSLN) has not been fully investigated. Therefore, the synchronization of MLSLN is concerned via feedback discrete-time observations control. Therein, we provide a novel Lyapunov functional for MLSLN. Moreover, the upper bound of the state observations interval duration is obtained. By making use of Lyapunov functional method, some techniques of inequality and graph theory, we derive some sufficient conditions to guarantee the mean-squared asymptotical synchronization of MLSLN. Then, the theoretical results are employed to study the synchronization of single-link robot arms. Meantime, numerical simulations are given to demonstrate the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

In this paper, based on Razumikhin method, stability of stochastic Lévy noise coupled systems with mixed delays (SLCSD) is researched. Here, both mixed delays and Lévy noise are considered into coupled systems for the first time. Then, by combining Razumikhin method with Lyapunov method and graph theory, several stability criteria including the Razumikhin-type theorem, the Lyapunov-type theorem and a coefficients-type theorem are given to ensure the pth moment exponential stability of SLCSD. In particular, the stability of a class of coupled oscillators and the stability of single-link robot arms are investigated as practical applications of the obtained results. And some numerical simulations are offered to illustrate the feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

This paper considers a general class of stochastic complex networks with time-varying delays (SCNTVDs). A systematic method of constructing a global Lyapunov function for the complex network is provided by combining graph theory and Lyapunov method. Consequently, some novel and simple sufficient conditions of exponential stability for the SCNTVDs are given. These conditions are presented in terms of the topological structure of networks. In addition, to illustrate the effectiveness and applicability of the proposed theory, a practical model in physics is studied and the numerical simulation is also given. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stabilisation of stochastic coupled systems (SCSs) via feedback control based on discrete-time state observations. State feedback control based on discrete-time observations is designed in the drift parts of the SCSs. Based on graph theory and Lyapunov method, the upper bound of the duration between two consecutive state observations is obtained. And a systematic method is given to construct a global Lyapunov function for SCSs via feedback control based on discrete-time state observations. A Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilisation in the sense of mean-square asymptotical stability and mean-square exponential stability. Furthermore, we use the theoretical results to analyse the stabilisation of stochastic coupled oscillators. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the developed theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses a stochastic coupled oscillators model. By employing the Lyapunov function method combined with Kirchhoff's Matrix Tree Theorem in graph theory, we establish a sufficient criterion to guarantee the existence of a stationary distribution for stochastic coupled oscillators. Moreover, a numerical example is given to illustrate the effectiveness of our theoretical results. • The problem we considered is the existence of a stationary distribution of a stochastic coupled oscillators model. • By using the Lyapunov method and Kirchhoff's Matrix Tree Theorem. • The approach we employ avoids constructing a Lyapunov function directly. [ABSTRACT FROM AUTHOR]

Multi-group models have attracted considerable attention due to their promising potential applications in various fields. In this paper, aperiodically intermittent control is designed to study the exponential stability of fractional-order multi-group models with dispersal. By applying Lyapunov method and graph theory, some sufficient conditions about exponential stability are established. From the theoretical results, we observe that the convergence speed depends on the control gain and the order of fractional derivative. Moreover, to show the practicality of theoretical results, we provide an application of modified fractional-order competitive neural networks. A stability criterion is also given to guarantee the exponential stability of modified fractional-order competitive neural networks. Finally, a numerical example is provided to show the effectiveness of the stated results. Some simulation comparisons are also carried out to illustrate the relationship between the convergence speed and the control gain with the order of fractional derivative. [ABSTRACT FROM AUTHOR]

In this paper, the exponential synchronization problem of complex-valued delayed coupled systems on networks with aperiodically on-off coupling is investigated. The on-off coupling is aperiodic, which takes the general on-off coupling as a special case. We analyze the complex-valued system directly by using R -Derivative and Conjugate R -Derivative. Then based on the Lyapunov method and graph theory, we give two kinds of synchronization criteria, which have a close relationship with the switch-on width of the coupling and the topological structure of the underlying network. Specially, when the switch-on width tends to zero, on-off coupling becomes impulsive control. Hence, the corresponding synchronization criteria under impulsive control are given as well. To illustrate the practicability of the main results, we apply the derived results to complex-valued delayed coupled oscillators. Finally, two numerical examples are given to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

• Multiple time-varying delay links are introduced into fractional-order competitive neural networks. • An integral inequality associated with every upper bound of each time-varying delay is proposed. • Based on integral inequality, a generalized fractional-order Halanay inequality is obtained. • The stability criterion is dependent on the topological structure of networks. Competitive neural networks have become increasingly popular since this kind of neural networks can better describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications. In this paper, we first propose fractional-order competitive neural networks with multiple time-varying-delay links and explore the global asymptotic stability of this class of neural networks. A novel and generalized integral inequality related to every upper bound of each time-varying delay is given. Moreover, based on Lyapunov method and graph theory, we obtain some sufficient conditions with the help of this integral inequality to guarantee the global asymptotic stability. The theoretical results offer a new perspective to show the close relationship between the stability criterion and the topological structure of networks. Finally, an illustrative numerical example is given to demonstrate the feasibility and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The existence of stationary distribution for stochastic coupled systems with regime switching and feedback control is investigated. In terms of model, feedback control is concerned in the existence of stationary distribution for stochastic coupled systems with regime switching. In terms of method, graph theory is employed to investigate the existence of stationary distribution for stochastic coupled systems with regime switching. And some sufficient conditions are given based on Lyapunov method connected with the graph theory and the M-matrix method to ensure the existence of stationary distribution, which reveals the influences that feedback control brings on stationary distribution and the existing area is related to stochastic disturbance, feedback control and coupling strength. Furthermore, the application to stochastic coupled oscillators with feedback control and regime switching can demonstrate the practicability of our theoretical results. Finally, a numerical example is presented to verify the effectiveness and availability of our results as well as the superiority of influence that feedback control brings on stationary distribution. • Feedback control is considered in the study of stationary distribution. • The existing area is affected by feedback control. • The theoretical results are applied to coupled oscillators. [ABSTRACT FROM AUTHOR]