An experimental survey of chaos and symmetry breaking in coupled and driven logistic maps

In this paper we report on the experimentally measured dynamics exhibited by a system comprised of two coupled circuits whose input-output relation follow the logistic-map function. The circuit takes in two external voltages that control the initial conditions, and we employ this capability to examine the phenomenon of symmetry breaking and to submit theoretical/numerical results on this dynamical system to experimental test. We demonstrate that symmetry-broken solutions manifest in this circuit for appropriately chosen initial conditions, and proceed to investigate experimentally the basins of attraction of these solutions, as well as their dependence on the coupling strength, . We illustrate the full power of this circuit by investigating the chaotic regime and by constructing experimental bifurcation diagrams. One intriguing phenomenon captured here involves the transition from synchronized chaos to decoherent chaos as the coupling is increased. Finally, we experimentally implement uni-directional coupling and explore the dynamics of a driven logistic map.