Convergent dynamics, a tribute to Boris Pavlovich Demidovich

Pavlov, Alexey; Pogromsky, Alexander Yu.; Wouw, Nathan van de; Nijmeijer, Henk

doi:10.1016/j.sysconle.2004.02.003

Cited by 296 publications

(233 citation statements)

References 11 publications

(12 reference statements)

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“…conditions is strongly related to the notions of 'convergent systems' [22] and 'contracting systems' [16]. However, the system (1) exhibits a weaker property than uniform contraction (which is imposed in [22,16] and related literature), and consequently the function V does not necessarily approach zero.…”

Section: Remark 2 As V (T) Equals the Square Of The Distance Between mentioning

confidence: 99%

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A mathematical model for the dynamics of clustering

Aeyels

Smet

2008

Physica D: Nonlinear Phenomena

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The formation of several clusters, arising from attracting forces between non-identical entities or agents, is a phenomenon observed in diverse fields. Think of people gathered through a mutual interest, swarm behavior of animals or clustering of oscillators in brain cells.We introduce a dynamical model of mutually attracting agents for which we prove that the long term behavior consists of agents organized into several groups or clusters. We have completely characterized the cluster structure (i.e. the number of clusters and their composition) by means of a set of inequalities in the parameters of the model and have identified the intensity of the attraction as a key parameter governing the transition between different cluster structures.The versatility of the model will be illustrated by discussing its relation to the Kuramoto model and by describing how it applies to a system of interconnected water basins.Pacs numbers: 89.75.Fb, 05.65.+b, 05.45.Xt

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Section: Remark 2 As V (T) Equals the Square Of The Distance Between mentioning

confidence: 99%

“…However, the system (1) exhibits a weaker property than uniform contraction (which is imposed in [22,16] and related literature), and consequently the function V does not necessarily approach zero.…”

Section: Remark 2 As V (T) Equals the Square Of The Distance Between mentioning

confidence: 99%

A mathematical model for the dynamics of clustering

Aeyels

Smet

2008

Physica D: Nonlinear Phenomena

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“…Such incremental stability analysis of signals was covered in [9], [10], [11]. In this paper, we prove that under the same coupling assumption as in [8], the differences between the outputs of interconnected, non-identical CFSs will asymptotically tend to finite, generally non-zero limits.…”

Section: Introductionmentioning

confidence: 79%

Robust synchronization in networks of cyclic feedback systems

Hamadeh

Stan

Gonçalves

2008

2008 47th IEEE Conference on Decision and Control

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Abstract-This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result.

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“…In Nuij et al [2006], Rijlaarsdam et al [2011a] the dynamics of a class of SISO convergent nonlinear systems [Pavlov et al, 2004] are considered when such system is subject to a sinusoidal input: u(t) = γ cos(2πξ 0 t + ϕ 0 ) (6) with γ, ϕ 0 ∈ R and ξ 0 ∈ R >0 . The output of such system is composed of K harmonics of the input frequency, i.e.…”

Section: Higher Order Sinusoidal Input Describing Functionsmentioning

confidence: 99%

New Connections Between Frequency Response Functions for a Class of Nonlinear Systems*

Rijlaarsdam

Oomen

Nuij

et al. 2012

IFAC Proceedings Volumes

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The notion of frequency response functions has been generalized to nonlinear systems in several ways. However, a relation between different approaches has not yet been established. In this paper, frequency domain representations for nonlinear systems are uniquely connected. Specifically, by means of novel analytical results, the generalized frequency response function (GFRF) and the higher order sinusoidal input describing function (HOSIDF) for polynomial Wiener-Hammerstein systems are explicitly related. Necessary and sufficient conditions for this relation to exist and results on uniqueness and equivalence of the HOSIDF and GFRF are provided. Finally, a numerically efficient computational procedure is presented that allows to compute the GFRF from the HOSIDF and vice versa.

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Convergent dynamics, a tribute to Boris Pavlovich Demidovich

Cited by 296 publications

References 11 publications

A mathematical model for the dynamics of clustering

A mathematical model for the dynamics of clustering

Robust synchronization in networks of cyclic feedback systems

New Connections Between Frequency Response Functions for a Class of Nonlinear Systems*

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