NDLI: Emergent Task Differentiation on Network Filters

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Saghafi, Mehdi Dankowicz, Harry Tabor, Whitney
Copyright Year	2017
Abstract	This paper aims to analyze the emergence of task differentiation in a model complex system, characterized by an absence of hierarchical control, yet able to exhibit coordinated behavior and collective function. The analysis focuses on linear network filters, i.e., networks of coupled linear oscillators with a differentiated steady-state response to exogenous harmonic excitation. It demonstrates how an optimal allocation of excitation sensitivities across the network nodes in a condition of resonance may be constructed either using global information about the network topology and spectral properties or through the iterated dynamics of a nonlinear, nonsmooth learning paradigm that only relies on local information within the network. Explicit conditions on the topology and desired resonant mode shape are derived to guarantee local asymptotic stability of fixed points of the learning dynamics. The analysis demonstrates the possibly semistable nature of the fixed point with all zero excitation sensitivities, a condition of system collapse that can be reached from an open set of initial conditions but that is unstable under the learning dynamics. Theoretical and numerical results also show the existence of periodic responses, as well as of connecting dynamics between fixed points, resulting in recurrent metastable behavior and noise-induced transitions along cycles of such connections. Structural additions to a core network that conserve desired spectral properties are proposed as a defensive mechanism for fault tolerance and shielding of the core against targeted harm.
Sponsorship	Division of Behavioral and Cognitive Sciences
Starting Page	1686
Ending Page	1709
Page Count	24
File Format	PDF
DOI	10.1137/16M1084432
e-ISSN	15360040
Issue Number	3
Volume Number	16
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2017-09-06
Access Restriction	Subscribed
Subject Keyword	piecewise-smooth system linear filter Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs division of labor Network models, deterministic network dynamics Dynamical systems in optimization and economics Programming involving graphs or networks
Content Type	Text
Resource Type	Article

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