A dual memristive Wien-bridge chaotic system with variable amplitude and frequency

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Electronic Engineering
• Cryptography

Background:

• Memristors are fundamental electronic components with memory properties.
• Chaotic systems exhibit complex, unpredictable behavior.
• Wien-bridge oscillators are widely used in electronics.

Purpose of the Study:

• To design and investigate a novel dual memristive Wien-bridge chaotic system.
• To explore the rich dynamic characteristics of the proposed system.
• To evaluate the system's potential for encryption applications.

Main Methods:

• Designing a dual memristive circuit using first-order generalized and polynomial memristors.
• Analyzing system dynamics using Lyapunov exponents, bifurcation diagrams, and phase portraits.
• Implementing the chaotic system on a digital signal processing (DSP) platform.
• Conducting the National Institute of Standards and Technology (NIST) test for randomness.

Main Results:

• The system exhibits complex dynamics, including transitions between periodic and chaotic states.
• Variable amplitude and frequency oscillations were observed.
• Coexisting attractors and locally sustained chaos were identified.
• The system passed the NIST randomness test, indicating suitability for cryptographic use.

Conclusions:

• The designed dual memristive Wien-bridge chaotic system demonstrates rich and complex dynamic behaviors.
• The system's ability to pass the NIST test highlights its potential for practical applications in encryption engineering.
• This research contributes to the development of novel chaotic systems for secure communication.