Existence of \(n\)-cycles and border-collision bifurcations in piecewise-linear continuous maps with applications to recurrent neural networks

DOI10.1007/s11071-020-05841-xzbMath1516.34072arXiv1911.04304MaRDI QIDQ6168793

Zahra Monfared, D. Durstewitz

Publication date: 9 August 2023

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.04304

zbMATH Keywords

stabilitychaosrecurrent neural networksmachine learningborder-collision bifurcations\(n\)-cyclespiecewise linear continuous maps

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (2)

Existence of \(n\)-cycles and border-collision bifurcations in piecewise-linear continuous maps with applications to recurrent neural networks ⋮ Unnamed Item

Cites Work

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• BORDER-COLLISION BIFURCATIONS IN ONE-DIMENSIONAL DISCONTINUOUS MAPS
• Multiple Attractor Bifurcation in Three-Dimensional Piecewise Linear Maps
• Dynamics of a piecewise linear map with a gap
• Existence of \(n\)-cycles and border-collision bifurcations in piecewise-linear continuous maps with applications to recurrent neural networks

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