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

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