NoLiTiA

NoLiTiA provides MATLAB implementations for nonlinear time series analysis to quantify dynamical invariants, recurrence structure, and information-theoretic measures in complex datasets.

Key Features:

• Comprehensive Methodological Range: Integrates methods from dynamical systems theory, recurrence quantification analysis (RQA), and information theory into a single MATLAB toolbox.
• Spatially and Time-Resolved Recurrence Amplitude Analysis: Implements recurrence amplitude analysis that resolves recurrence structures across space and time for nuanced pattern detection.
• Dynamical Systems Theory: Provides tools for estimating dynamic invariants such as Lyapunov exponents to assess stability and chaos.
• Recurrence Quantification Analysis (RQA): Analyzes recurrence properties of phase space trajectories to characterize system dynamics.
• Information Theory Measures: Includes entropy-based metrics such as active information storage to quantify information processing in time series.
• Time-Resolved Aperiodic Oscillation Quantification: Supports recent methods for quantifying time-resolved aperiodic oscillations in signals.

Scientific Applications:

• Neuroscience: Applied to analyze complex neuronal and brain time series dynamics using nonlinear and information-theoretic measures.
• Climatology: Used to characterize nonlinear dynamics and recurrence structures in climate-related time series.
• Physics: Employed to study dynamical invariants, chaos, and recurrence behavior in physical systems.

Methodology:

Implements dynamical systems analysis including Lyapunov exponent estimation, recurrence quantification analysis and spatial/time-resolved recurrence amplitude analysis, entropy-based information measures such as active information storage, and methods for quantifying time-resolved aperiodic oscillations of phase space trajectories.