Complex dynamics induced by a sine nonlinearity in a five-term chaotic system: FPGA hardware design and...

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Complex Systems Analysis
• Mathematical Modeling

Background:

• The Rössler prototype-4 equations serve as a foundation for exploring complex dynamical systems.
• Sine nonlinearity offers a unique approach to designing chaotic models with simplified structures.
• Understanding chaotic behavior is crucial for developing advanced applications in various fields.

Purpose of the Study:

• To introduce a new five-term chaotic model derived from the Rössler prototype-4 equations.
• To analyze the complex dynamics of the proposed system using established nonlinear tools.
• To investigate the model's potential for practical applications through implementation studies.

Main Methods:

• Derivation of a novel five-term chaotic system utilizing sine nonlinearity.
• Analysis of system dynamics through bifurcation diagrams, Lyapunov exponents spectra, and frequency power spectra.
• Examination of basins of attraction to understand coexisting attractors.

Main Results:

• The proposed model exhibits elegant algebraic simplicity while displaying complex chaotic dynamics.
• The system can generate infinitely many identical chaotic attractors and limit cycles.
• Up to six nontrivial coexisting attractors were observed, demonstrating rich dynamic behavior.
• Feasibility for analog and digital chaos-based applications was confirmed through circuit and FPGA implementation discussions.

Conclusions:

• The new chaotic model offers a unique combination of simplicity and complex dynamics.
• Its adjustable equilibrium points and ability to generate multiple attractors make it versatile.
• The demonstrated implementation potential highlights its suitability for real-world chaos-based engineering applications.