Chaotic maps derived from trajectory data.

Area of Science:

• Dynamical Systems
• Nonlinear Dynamics
• Data Analysis

Background:

• Characterizing discrete time dynamical processes is crucial for understanding complex systems.
• Observed trajectory data often provides incomplete information, such as a rough phase plot, probability density function, and metric entropy.

Purpose of the Study:

• To develop a method for constructing a nonlinear map that accurately represents observed dynamical system properties.
• To ensure the constructed map aligns with the phase plot, probability density function, and metric entropy derived from trajectory data.

Main Methods:

• Utilizing observed trajectory data to infer properties of a discrete time dynamical process.
• Developing a nonlinear map construction technique constrained by the phase plot, probability density function, and metric entropy.
• Validating the constructed map against the observed data characteristics.

Main Results:

• A method for generating a nonlinear map from trajectory data was successfully described.
• The constructed nonlinear map was shown to be consistent with the rough phase plot of the observed data.
• The method ensures the resulting map preserves the observed probability density function and metric entropy.

Conclusions:

• The proposed method effectively reconstructs a nonlinear map that encapsulates key features of a discrete dynamical process from trajectory data.
• This approach offers a way to model complex systems when only partial observational data is available.
• The technique provides a robust framework for inferring dynamical system behavior and properties.