Fast synchronization of complex dynamical networks with time-varying delay via periodically intermittent control

The fast synchronization problem for a class of complex dynamical networks with time varying delay by means of periodically intermittent control is studied. Based on the finite-time stability theory and periodically intermittent control technique, some sufficient synchronization criteria are obtained to guarantee the fast synchronization. Furthermore, the essential condition for guaranteeing periodically intermittent control realized in finite time is given in this paper. Finally, two examples are illustrated to verify the proposed theoretical results.http://www.elsevier.com/locate/neucom2017-09-30hb2016Electrical, Electronic and Computer Engineerin

Exponential Synchronization of Complex Delayed Dynamical Networks With Switching Topology

This paper studies the local and global exponential synchronization of a complex dynamical network with switching topology and time-varying coupling delays. By using stability theory of switched systems and the network topology, the synchronization of such a network under some special switching signals is investigated. Firstly, under the assumption that all subnetworks are self-synchronizing, a delay-dependent sufficient condition is given in terms of linear matrix inequalities, which guarantees the solvability of the local synchronization problem under an average dwell time scheme. Then this result is extended to the situation that not all subnetworks are self-synchronizing. For the latter case, in addition to average dwell time, an extra condition on the ratio of the total activation time of self-synchronizing and nonsynchronizing subnetworks is needed to achieve synchronization of the entire switched network. The global synchronization of a network whose isolate dynamics is of a particular form is also studied. Three different examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results. © 2006 IEEE.published_or_final_versio

Exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays via periodically intermittent control

This paper deals with the exponential synchronization problem for reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, a periodically intermittent controller is first proposed to guarantee the exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance in terms of p-norm. The obtained synchronization results are easy to check and improve upon the existing ones. Particularly, the traditional assumptions on control width and time-varying delays are removed in this paper. This paper also presents two illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme

Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control

Synchronization of reaction–diffusion Hopfield neural networks with s-delays via sliding mode control (SMC) is investigated in this paper. To begin with, the system is studied in an abstract Hilbert space C([–r; 0];U) rather than usual Euclid space Rn. Then we prove that the state vector of the drive system synchronizes to that of the response system on the switching surface, which relies on equivalent control. Furthermore, we prove that switching surface is the sliding mode area under SMC. Moreover, SMC controller can also force with any initial state to reach the switching surface within finite time, and the approximating time estimate is given explicitly. These criteria are easy to check and have less restrictions, so they can provide solid theoretical guidance for practical design in the future. Three different novel Lyapunov–Krasovskii functionals are used in corresponding proofs. Meanwhile, some inequalities such as Young inequality, Cauchy inequality, Poincaré inequality, Hanalay inequality are applied in these proofs. Finally, an example is given to illustrate the availability of our theoretical result, and the simulation is also carried out based on Runge–Kutta–Chebyshev method through Matlab

Pseudo-laminar chaos from on-off intermittency

In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from delay systems with lag-time modulation. Applying, however, to such systems a test for laminar chaos, as proposed in [Phys. Rev. E 101, 032213 (2020)], these signals fail such test, thus leading to the notion of pseudo-laminar chaos. The latter can be interpreted as integrated periodically driven on-off intermittency. We demonstrate that, on a signal level, true laminar and pseudo-laminar chaos are hardly distinguishable in systems with and without dynamical noise. However, very pronounced differences become apparent when correlations of signals and increments are considered. We compare and contrast these properties of pseudo-laminar chaos with true laminar chaos.Comment: 13 pages, 7 figure