TY - JOUR
T1 - Emergent task differentiation on network filters
AU - Sagha, Mehdi
AU - Dankowicz, Harry
AU - Tabor, Whitney
N1 - ∗Received by the editors July 12, 2016; accepted for publication (in revised form) March 23, 2017; published electronically September 6, 2017. http://www.siam.org/journals/siads/16-3/M108443.html Funding: This material is based upon work supported by the National Science Foundation under grant BCS-1246920. †Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 ([email protected], [email protected]). ‡Department of Psychology, University of Connecticut, Storrs, CT 06269 ([email protected]).
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Division of labor
KW - Linear filter
KW - Network dynamics
KW - Piecewise-smooth system
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U2 - 10.1137/16M1084432
DO - 10.1137/16M1084432
M3 - Article
AN - SCOPUS:85031789441
SN - 1536-0040
VL - 16
SP - 1686
EP - 1709
JO - SIAM Journal on Applied Dynamical Systems
JF - SIAM Journal on Applied Dynamical Systems
IS - 3
ER -