A 2D hyperchaotic map with conditional symmetry and attractor growth.

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Complex Systems Analysis

Background:

• Chaotic maps are fundamental in understanding complex systems.
• Existing chaotic maps often lack specific properties like conditional symmetry or controllable attractor dynamics.

Purpose of the Study:

• To construct a novel 2D hyperchaotic map with unique properties.
• To investigate the existence of conditional symmetric and asymmetric hyperchaotic attractors.
• To explore attractor growth and polarity balance restoration in discrete chaotic systems.

Main Methods:

• Introduction of trigonometric functions to create a 2D discrete map.
• Analysis of conditional symmetric and asymmetric hyperchaotic attractors.
• Investigation of attractor growth under periodic feedback.
• Application of sinusoidal functions and constant term inversion for polarity balance.
• Hardware implementation using STM32 for validation.

Main Results:

• A novel 2D hyperchaotic map was successfully constructed.
• The map exhibits both symmetric and asymmetric hyperchaotic attractors.
• Attractor growth was observed under specific periodic feedback conditions.
• Polarity balance was restored using sinusoidal functions and constant term inversion.
• Hardware implementation results validated the numerical simulations and theoretical analysis.

Conclusions:

• The proposed 2D hyperchaotic map possesses unique properties not found in other chaotic maps.
• The map's characteristics make it a promising candidate for applications in secure communications and cryptography.
• The successful hardware implementation demonstrates the practical feasibility of the proposed chaotic system.