  In many scientific fields like e.g. neuroscience, climatology or physics,
complex relationships can be described most parsimoniously by nonlinear
mechanics. Despite their relevance, many scientists still apply linear
estimates in order to evaluate complex interactions. This is partially due to
the lack of a comprehensive compilation of nonlinear methods. Available
packages mostly specialize in only one aspect of nonlinear time-series analysis
and most often require some coding proficiency to use. Here, we introduce
NoLiTiA, a free open-source MATLAB toolbox for nonlinear time series analysis.
In comparison to other currently available nonlinear packages, NoLiTiA offers
1) an implementation of a broad range of classic and recently developed
methods, 2) an implementation of newly proposed spatially and time-resolved
recurrence analysis and 3) an intuitive environment accessible even to users
with little coding experience due to a graphical user interface and
batch-editor. The core methodology derives from three distinct fields of
complex systems theory, including dynamical systems theory, recurrence
quantification analysis and information theory. Besides established methodology
including estimation of dynamic invariants like Lyapunov exponents and
entropy-based measures, such as active information storage, we include recent
developments of quantifying time-resolved aperiodic oscillations. In general,
the toolbox will make nonlinear methods accessible to the broad scientific
community engaged in time series processing.
