Using an Arduino in a Coupled Logistic Map Circuit to Explore Basins of Attraction for Symmetry-broken States

L’Her et al. [1] recently constructed a circuit designed to implement the logistic map electronically, and thus generated bifurcation diagrams in growth rate, r, as well as in coupling parameter, ε, for two coupled maps. We show that in the coupled logistic-map system, the dynamics is not only determined by r and ε, but also by the initial conditions, due to the multi-stability of different solutions. By experimentally adding control over initial conditions and incorporating an Arduino Uno Microcontroller, we explore basins of attraction associated with symmetric states, symmetry-broken states and phase-shifted states.

[1] L’Her, A., et al., Eur. Phys. J. B (2016) 89: 81