FPAA-based implementation of fractional-order chaotic oscillators using first-order active filter blocks.

Area of Science:

• Nonlinear Dynamics
• Analog Circuit Design
• Chaos Theory

Background:

• Fractional-order chaotic oscillators (FOCOs) are typically implemented on digital hardware like FPGAs.
• Digital implementations face limitations due to finite bit precision, potentially degrading chaotic behavior.
• Analog implementations offer an alternative for generating continuous-time chaotic signals.

Purpose of the Study:

• To implement FOCOs using analog electronics for continuous-time chaotic behavior generation.
• To overcome the limitations of digital hardware in FOCO implementations.
• To demonstrate the feasibility of using Field-Programmable Analog Arrays (FPAAs) for analog FOCOs.

Main Methods:

• Applied Charef's method to approximate fractional-order derivatives as polynomial ratios in the Laplace domain.
• Analyzed two commensurate FOCOs, determining equilibrium points and eigenvalues to estimate minimum fractional orders for chaos.
• Designed polynomial approximations using first-order all-pass and low-pass filters implemented with amplifiers.

Main Results:

• Successfully synthesized and implemented FOCOs on an FPAA device.
• Experimental results closely matched simulation outcomes, validating the analog approach.
• Demonstrated the FPAA's capability for generating continuous-time chaos and reprogramming FOCO parameters.

Conclusions:

• Analog implementation of FOCOs using FPAAs is a viable method for generating continuous-time chaotic behavior.
• FPAAs provide a flexible platform for prototyping and modifying analog chaotic oscillators.
• This approach overcomes digital precision limitations, offering a robust alternative for chaos generation.