Small, fully reproducible systems whose information-theoretic behaviour is familiar from the literature. These are illustrative rather than validation, and the parity suite covers accuracy. Every curve is computed with infomeasure and drawn here as inline SVG.
The logistic map xt+1 = r xt(1 − xt) is the textbook route to chaos. Its order-3 permutation entropy drops at the periodic windows and rises in the chaotic bands. The two estimators have different offsets, so both curves are min-max normalised over the parameter range to make their shapes comparable.
A population of phase oscillators with heterogeneous frequencies synchronises as the coupling grows. Mutual information and transfer entropy between two oscillators rise through the transition and the estimators agree in the ordered phase.
Two unidirectionally coupled Rossler systems are a standard test for causal inference. The signed difference of forward and backward transfer entropy is positive when the coupling direction is recovered. The parametric Renyi and Tsallis families expose a dependence on their parameters that the Shannon estimators cannot.