On Bifurcations Along the Spiral Organization of the Periodicity in a Hopfield Neural Network

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Communications in Advanced Mathematical Sciences
Volume:5 Issue:2
On Bifurcations Along the Spiral Organization of the Periodicity in a Hopfield Neural Network

On Bifurcations Along the Spiral Organization of the Periodicity in a Hopfield Neural Network

Authors : Angela DA SİLVA, Paulo RECH

Pages : 92-98

Doi:10.33434/cams.1064713

View : 42 | Download : 12

Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :In this work we report numerical results involving a certain Hopfield-type three-neurons network, with the hyperbolic tangent as the activation function. Specifically, we investigate a place of a two-dimensional parameter-space of this system where typical periodic structures, the so-called shrimps, are embedded in a chaotic region. We show that these structures are organized themselves as a spiral that coil up toward a focal point, while undergo period-adding bifurcations. We also indicate the locations along this spiral in the parameter-space, where such bifurcations happen.
Keywords : Chaos, Lyapunov exponents spectrum, Parameter space, Period adding bifurcation

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