Mesocopic comparison of complex networks based on periodic orbits

Area of Science:

• Dynamical systems theory
• Network science
• Animal behavior

Background:

• Complex noiseless dynamical systems are often represented by unstable periodic orbits.
• Existing methods lack ways to measure similarity or extend to noisy systems and complex networks.

Purpose of the Study:

• To develop a method for analyzing complex dynamical systems using unstable periodic orbits.
• To extend this method to noisy systems and complex networks.
• To apply the method to understand animal communication.

Main Methods:

• Utilized unstable periodic orbits for compressed representation of dynamical systems.
• Developed a novel approach to quantify similarity and handle noisy systems.
• Applied the method to analyze Drosophila precopulatory courtship behavior.

Main Results:

• The method successfully represents complex systems and quantifies similarity.
• It is applicable to noisy systems and complex networks.
• Analysis of Drosophila courtship revealed a complex grammatical structure.

Conclusions:

• The developed method provides a novel way to analyze complex dynamical systems.
• The discovered grammar in Drosophila courtship is highly unlikely to be random.
• This suggests sophisticated communication rules in animal behavior.