Characterizing complexity of non-invertible chaotic maps in the Shannon-Fisher information plane with ordinal patterns

Being able to distinguish the different types of dynamics present in a given nonlinear system is of great importance in complex dynamics. It allows to characterize the system, find similarities and differences with other nonlinear systems, and classify those dynamical regimes to understand them better. For systems that develop chaos it is not always easy to distinguish determinism from stochasticity. We analyze several non-invertible maps by projecting them on the two-dimensional Fisher-Shannon plane using ordinal patterns. We find that this technique unfolds the complex structure of chaotic systems, showing more details than other methods. It also reveals signatures common to most of the non-invertible maps, and demonstrates its capability to distinguish determinism from stochasticity. (C) 2020 Elsevier Ltd. All rights reserved.