In this paper, by using pinning impulse controller and hybrid controller respectively, the research difficulties of asymptotic synchronization and finite time cluster synchronization of time-varying delayed neural networks are studied. On the ground of Lyapunov stability theorem and Lyapunov-Razumikhin method, a novel sufficient criterion on asymptotic cluster synchronization of time-varying delayed neural networks is obtained. Utilizing Finite time stability theorem and hybrid control technology, a sufficient criterion on finite-time cluster synchronization is also obtained. In order to deal with time-varying delay and save control cost, pinning pulse control is introduced to promote the realization of asymptotic cluster synchronization. Following the idea of pinning control scheme, we design a progressive hybrid control to promote the realization of finite time cluster synchronization. Finally, an example is given to illustrate the theoretical results.
In this paper, we propose several models, which can realize synchronization of complex networks in finite time effectively. The results apply to heterogeneous dynamic networks, too. The mechanism of finite time convergence is revealed. Different from many models, which assume the coupling matrix being symmetric (or the connecting graph is undirected), here, the coupling matrix is asymmetric (or the connecting graph is directed).
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial order) and a "topological" condition on the maps. Then, we prove the existence of a pullback random attractor whose distribution is the unique stationary measure of the random iteration, and we obtain the synchronization of random orbits. As a consequence of the synchronization phenomenon, a functional central limit theorem is established.
This paper presents an innovative hybrid systems approach to the sender-receiver synchronization of timers. Via the hybrid systems framework, we unite the traditional sender-receiver algorithm for clock synchronization with an online, adaptive strategy to achieve synchronization of the clock rates to exponentially synchronize a pair of clocks connected over a network. Following the conventions of the algorithm, clock measurements of the nodes are given at periodic time instants, and each node uses these measurements to achieve synchronization. For this purpose, we introduce a hybrid system mod…
In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization and coupling structure is studied. Conditions on the interconnection under which synchronization can be achieved for some selection of coupling strengths are established. How to strengthen those conditions so that synchronization is guaranteed for all admissible parameter values is also presented.
This paper presents a distributed hybrid algorithm that synchronizes the time and rate of a set of clocks connected over a network. Clock measurements of the nodes are given at aperiodic time instants and the controller at each node uses these measurements to achieve synchronization. Due to the continuous and impulsive nature of the clocks and the network, we introduce a hybrid system model to effectively capture the dynamics of the system and the proposed hybrid algorithm. Moreover, the hybrid algorithm allows each agent to estimate the skew of its internal clock in order to allow for synchro…
In this article, a new synchronization scheme is presented by combining the concept of reduced-order synchronization with multi-switching synchronization schemes. The presented scheme, reduced-order multi-switching hybrid synchronization, is notable addition to the earlier multi-switching schemes providing enhanced security in applications of secure communication. Based on the Lyapunov stability theory, the active control method is used to design the controllers and derive sufficient condition for achieving reduced-order multi-switching hybrid synchronization between a new hyperchaotic system …
In our previous work [Chiba, Medvedev, arXiv:1612.06493], we initiated a mathematical investigation of the onset of synchronization in the Kuramoto model (KM) of coupled phase oscillators on convergent graph sequences. There, we derived and rigorously justified the mean field limit for the KM on graphs. Using linear stability analysis, we identified the critical values of the coupling strength, at which the incoherent state looses stability, thus, determining the onset of synchronization in this model. In the present paper, we study the corresponding bifurcation. Specifically, we show that sim…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network is allowed to contain interior nodes, i.e., those that are not directly connected to an oscillator. It is shown that the oscillators asymptotically synchronize if and only if the Schur complement (with respect to the boundary nodes) of the complex-valued Laplacian matrix representing the coupling has a single eigenvalue on the imaginary axis.
In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data is confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in \cite{H-L-Z20} to capture a clear hierarchical structure, which successfully yields the dissipation mechanism of phase diameter and a small invariant set after finite time. Then the dissipation of frequency diameter will be clear, which ev…
This work investigates the synchronization between two chaotic food webs using the generalized Lotka-Volterra (GLV) model consisting of one prey and two predator populations. We, first, examine the impact of three functional responses (linear, Holling type II, and Holling type III) on system dynamics For the study, we consider the model with a linear functional response consisting of chaotic oscillations and apply controllers to stabilize its unstable fixed points. This research contributes to the understanding of how to apply chaotic ecological models to predict the population of competing sp…
We discuss the asymptotic frequency synchronization for the non-identical Kuramoto oscillators with time delayed interactions. We provide explicit lower bound on the coupling strength and upper bound on time delay in terms of initial configurations ensuring exponential synchronization. This generalizes not only the frequency synchronization estimate by Choi et al. [Physica D, 241, (2012), 735-754] for the non-identical Kuramoto oscillators without time delays but also improves previous result by Schmidt et al. [Automatica, 48, (2012), 3008-3017] in the case of homogeneous time delays where the…
