This technical note addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this technical note, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.
Synchronization transitions are investigated in small-world neuronal networks that are locally modeled by the Rulkov map with additive spatiotemporal noise. In particular, we investigate the impact of different information transmission delays and rewiring probability. We show that short delays induce zigzag fronts of excitations, whereas intermediate delays can further detriment synchrony in the network due to a dynamic clustering anti-phase synchronization transition. Detailed investigations reveal, however, that for longer delay lengths the synchrony of excitations in the network can again be enhanced due to the emergence of in-phase synchronization. In addition, we show that an appropriate small-world topology can restore synchronized behavior provided information transmission delays are either short or long. On the other hand, within the intermediate delay region, which is characterized by anti-phase synchronization and clustering, differences in the network topology do not notably affect the synchrony of neuronal activity.
This paper addresses the distributed containment control problem for a linear multi-leader multi-agent system with a directed communication topology. A new class of distributed observer-type containment protocols based only on the relative output measurements of the neighboring agents is proposed, removing the impractical assumption in some of the existing approaches that the observers embedded in the multiple dynamic agents have to share information with their neighbors. Under the mild assumption that, for each follower, there exists at least one leader having a directed path to that follower, some sufficient conditions are derived to guarantee the states of the followers to asymptotically converge to a convex hull formed by those of the dynamic leaders. Finally, some numerical simulations on containment of a multi-vehicle system are given to verify the effectiveness of the theoretical results.Index Terms-Networked system, multi-leader system, containment control, observer-type protocol, multi-vehicle system, communication.0018-9286 (c)
We study the effects of periodic subthreshold pacemaker activity and time-delayed coupling on stochastic resonance over scale-free neuronal networks. As the two extreme options, we introduce the pacemaker respectively to the neuron with the highest degree and to one of the neurons with the lowest degree within the network, but we also consider the case when all neurons are exposed to the periodic forcing. In the absence of delay, we show that an intermediate intensity of noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble, irrespective to its placing, thus providing evidences for stochastic resonance on the scale-free neuronal networks. Interestingly thereby, if the forcing in form of a periodic pulse train is introduced to all neurons forming the network, the stochastic resonance decreases as compared to the case when only a single neuron is paced. Moreover, we show that finite delays in coupling can significantly affect the stochastic resonance on scale-free neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances independently of the placing of the pacemaker, but they can also altogether destroy stochastic resonance. Delay-induced multiple stochastic resonances manifest as well-expressed maxima of the correlation measure, appearing at every multiple of the pacemaker period. We argue that fine-tuned delays and locally active pacemakers are vital for assuring optimal conditions for stochastic resonance on complex neuronal networks. It is well known that noise can play a constructive role in different types of nonlinear dynamical systems, and stochastic resonance is perhaps the most prominent example of this fact. The objective of this article is to extend the scope of stochastic resonance to complex networks, whereby the deterministic periodic input is not only limited in its strength but also its outreach. More precisely, scale-free neuronal networks are studied on which the subthreshold periodic forcing is introduced only to a single neuron of the network, thus acting as a pacemaker. We want to determine to what extent the complex scale-free topology can aid the pacemaker to entrain the complete neuronal ensemble with the help of fine-tuned additive noise. Moreover, the new findings are compared with results obtained via the more traditional setup where every neuron of the network is subjected to a weak periodic forcing. It is found that scale-free topologies are very efficient in propagating noise-supported localized weak rhythmic activities. Also, it is found that these paced networks are superior to globally forced networks in that stochastic resonance is better expressed on the former. Importantly, since time delays are inherent to the nervous system we take this explicitly into account via time-delayed coupling. We report on the occurrence of delay-induced multiple stochastic resonances on scale-free neuronal networks, which appear due to the locking between the delay length and the oscillation period of the pacemaker.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.