Design and DSP implementation of structurally non-uniform multi-scroll attractors based on novel modified sawtooth...

Area of Science:

• Non-linear dynamics
• Chaos theory
• Complex systems

Background:

• Conventional multi-scroll chaotic systems (MSCSs) have uniform scroll distributions, limiting attractor diversity.
• Non-uniform MSCSs offer greater flexibility in attractor configuration for engineering applications.

Purpose of the Study:

• To propose and investigate novel non-uniform multi-scroll attractors with irregular spatial distributions.
• To explore the generation mechanisms and offset-boosting phenomenon of these attractors.
• To validate the chaotic characteristics and practical applicability of the proposed systems.

Main Methods:

• Embedding five modified sawtooth wave functions into a 3D chaotic system.
• Generating five types of non-uniform multi-scroll attractors and four types of grid attractors.
• Analyzing attractor generation, offset-boosting, chaotic characteristics (Lyapunov exponent, bifurcation diagrams, spectral entropy), and randomness (NIST test).
• Hardware implementation on a digital signal processing platform.

Main Results:

• Successfully generated diverse non-uniform multi-scroll attractors with unique spatial distributions.
• Observed attractor coexistence in specific configurations (central separation, separated scrolls with enlarged sides, cross-shaped grid).
• Demonstrated the offset-boosting phenomenon and confirmed chaotic characteristics through rigorous analysis.
• Validated system randomness using the NIST test and confirmed practical applicability via hardware implementation.

Conclusions:

• The proposed modified sawtooth wave functions effectively generate novel non-uniform multi-scroll attractors with enhanced diversity.
• These systems exhibit desirable chaotic properties and practical engineering potential, confirmed by analysis and hardware implementation.
• The study advances the field of chaotic systems by offering more flexible and complex attractor structures.