A Periodically Forced Wilson–Cowan System with Multiple Attractors

DOI10.1137/110823365zbMath1318.92005OpenAlexW2051939328MaRDI QIDQ2904729

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Publication date: 23 August 2012

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/110823365

zbMATH Keywords

periodic forcingPoincaré mappitchfork bifurcationmultiple attractorscubic-like differential equationslope field symmetryWilson-Cowan system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Neural networks for/in biological studies, artificial life and related topics (92B20) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (5)

Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model ⋮ Analysis of chaotic oscillations induced in two coupled Wilson-Cowan models ⋮ Almost periodic solutions for Wilson-Cowan type model with time-varying delays ⋮ Periodic Forcing of Inhibition-Stabilized Networks: Nonlinear Resonances and Phase-Amplitude Coupling ⋮ Complexity induced by external stimulations in a neural network system with time delay

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