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A note on fractional feed‐forward networks
Author(s) -
Pinto Carla M. A.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3817
Subject(s) - mathematics , fractional calculus , hopf bifurcation , order (exchange) , derivative (finance) , bifurcation , nonlinear system , aka , realization (probability) , mathematical analysis , value (mathematics) , computer science , physics , statistics , finance , quantum mechanics , library science , financial economics , economics
We simulate a fractional feed‐forward network. This network consists of three coupled identical ‘cells’ (aka, oscillators). We study the behaviour of the associated coupled cell system for variation of the order of the fractional derivative, 0 < α < 1. We consider the Caputo derivative, approximated by the Grünwald–Letnikov approach, using finite differences of fractional order. There is observed amplification of the small signals by exploiting the nonlinear response of each oscillator near its intrinsic Hopf bifurcation point for each value of α . The value of the Hopf bifurcation point varies with the order of the fractional derivative α . Copyright © 2016 John Wiley & Sons, Ltd.