Dynamical properties of the composed Logistic-Gauss map.

Area of Science:

• Dynamical Systems and Chaos Theory
• Nonlinear Dynamics
• Mathematical Physics

Background:

• Dissipative mappings exhibit complex behaviors, including periodic and chaotic regions.
• Understanding the parameter space is crucial for characterizing these dynamics.
• Extreme orbits offer insights into the structural organization of one-dimensional maps.

Purpose of the Study:

• To analyze the unique composition of the Logistic-Gauss map.
• To explore its parameter space for complex periodic structures and chaotic regions.
• To investigate the role of extreme orbits in understanding system behavior.

Main Methods:

• Composition of the Logistic-Gauss map.
• Exploration of the parameter space by manipulating control parameters.
• Identification and analysis of extreme orbits and Complex Sets of Periodicity (CSP).

Main Results:

• Discovery of Complex Sets of Periodicity (CSP) within the parameter space.
• Identification of superstable curves characterizing CSP structures.
• Observation of cascades of CSP structures with added periods, organized by extreme curves.

Conclusions:

• The Logistic-Gauss map exhibits intricate dynamics with organized periodic structures.
• Extreme orbits are key to understanding the structural organization and system behavior.
• This research expands the understanding of chaos and periodicity in dissipative mappings.