The impact of competing time delays in coupled stochastic systems

Hunt, David; Korniss, G.; Szymanski, Boleslaw K.

doi:10.1016/j.physleta.2010.12.060

Cited by 18 publications

(11 citation statements)

References 50 publications

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“…9 in the (τ o , τ ) plane. In this simple case of two coupled nodes, the synchronization boundary is monotonic, and the local delay is dominant: There is no singularity (for any finite τ tr ) as long as στ o < 1/2 [66], while for any τ tr , there is a sufficiently large τ o resulting in the breakdown of synchronization. For N ≥ 3, the phase diagram (region of synchronizability) can be obtained numerically by tracking the zeros of the characteristic equation Eq.…”

Section: A Fully-connected Networkmentioning

confidence: 99%

Network coordination and synchronization in a noisy environment with time delays

2012

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We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.

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Section: A Fully-connected Networkmentioning

confidence: 99%

Network coordination and synchronization in a noisy environment with time delays

2012

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“…Remark 5.2: Performance of first-order consensus network with C = Mn was previously approximated in [25], [40] by using heuristic methods. We have utilized a systematic method to provide an approximate function (36) and we refer to [41] for more details.…”

Section: A Cost Function Approximation and Sdp Relaxationmentioning

confidence: 99%

Performance Improvement in Noisy Linear Consensus Networks With Time-Delay

Ghaedsharaf

Siami

Somarakis

et al. 2019

IEEE Trans. Automat. Contr.

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We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. The performance is measured by network's square of H 2 -norm and it is shown that it is a convex function of Laplacian eigenvalues and the coupling weights of the underlying graph of the network. First, we propose a tight convex, but simple, approximation of the performance measure in order to achieve lower complexity in our design problems by eliminating the need for eigen-decomposition. The effect of time-delay reincarnates itself in the form of non-monotonicity, which results in nonintuitive behaviors of the performance as a function of graph topology. Next, we present three methods to improve the performance by growing, re-weighting, or sparsifying the underlying graph of the network. It is shown that our suggested algorithms provide near-optimal solutions with lower complexity with respect to existing methods in literature.performance measure for network synthesis, (iii) low time complexity algorithms to design state feedback controllers for performance enhancement of time-delay linear consensus networks. In section III, we express the H2-norm performance of a time-delay linear consensus network in terms of its Laplacian spectrum. Furthermore, we prove that this performance measure is convex with respect to coupling weights and Laplacian spectrum, and in addition, it is an increasing function of time-delay. In section IV, we discuss topologies with optimal performance. Furthermore, we quantify a sharp lower bound on the best achievable performance for a network with a fixed timedelay. In presence of time-delay, the H2-norm performance of firstorder consensus network is not monotone decreasing with respect to connectivity, which impose challenges in design of the optimal network as increasing connectivity may deteriorate the performance. Then, we present methods to improve the performance measure. We categorize these procedures as growing, reweighting, and sparsification. Although the H2-norm performance is a convex function of Laplacian eigenvalues, direct use of this spectral function in our network design problems requires eigen-decomposition, which adds to time complexity of our design procedures. To overcome this, our key idea is to calculate an approximation function of the performance measure that spares us eigen-decomposition of the Laplacian matrix. In section V, we tackle the combinatorial problem of improving the non-monotone performance measure of the time-delay network by adding new interconnection links. Our time-complexity analysis of our proposed algorithm to grow a time-delay network shows that it can be done in O(n 3 + mn 2 + kn 2 ) arithmetic operations, where n is number of nodes, m is number of rows of the output matrix C and k is maximum number of new interconnections. Section VI discusses reweighting of the coupling weights as an approach to improve the performance measure. This design problem can be cast as a semidefinite programming (SD...

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“…T ∈ R n , and A is also known as the configuration matrix [18,30]. Equations (1) and (2) have been broadly studied in the literature in the context of neural networks [4], synchronization [15,16,35], traffic flow [5,6,37], and autonomous agents [18,[29][30][31]34,38,39]. Different than the earlier work, here we consider the graph as a parameter in the analysis of synchronization dynamics, and thus the objective here is to reveal how graphs corresponding to large dimensional A could be synthesized based on the eigenvalues of A, while assuring that the dynamics in Eq.…”

Section: A Synchronization Model With Delaymentioning

confidence: 99%

“…Nevertheless, synchronizability, delays, and graph structures are all interrelated, and thus need to be studied in an ensemble [29,32,33]. This observation motivates the paper, in which we take the equilibrium behavior of a synchronization dynamics studied * rifat@coe.neu.edu broadly in the literature [15,16,18,30,31,34,35] and explain the synchronizability (stability) features of the equilibrium in connection with (i) for how much delays synchronizability can still hold and (ii) how the corresponding graph structures can be tailored while still maintaining synchronizability.…”

Section: Introductionmentioning

confidence: 98%

Rules and limitations of building delay-tolerant topologies for coupled systems

Wang

Sipahi

2012

Phys. Rev. E

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This paper investigates the equilibrium behavior of broadly studied synchronization dynamics of coupled systems, among which shared information is delayed. The underlying relationship is established between graph structures and the largest amount of delay the dynamics can withstand without losing stability. In particular, based on Cartesian product of graphs, we present the rules and limitations for synthesizing the graphs of large-scale systems that can remain stable for as large delays as possible. Examples are provided to demonstrate the results.

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The impact of competing time delays in coupled stochastic systems

Cited by 18 publications

References 50 publications

Network coordination and synchronization in a noisy environment with time delays

Network coordination and synchronization in a noisy environment with time delays

Performance Improvement in Noisy Linear Consensus Networks With Time-Delay

Rules and limitations of building delay-tolerant topologies for coupled systems

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