Memristor-type chaotic mapping

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Electronic Engineering and Circuit Design
• Memristor Applications

Background:

• Memristors are fundamental electronic components with unique memory properties.
• Discrete chaotic systems are crucial for secure communications and complex simulations.
• Existing chaotic systems often lack efficient amplitude control mechanisms.

Purpose of the Study:

• To design and analyze a novel memristor-type chaotic mapping.
• To investigate the amplitude control capabilities of system parameters.
• To demonstrate the feasibility of the proposed chaotic system through hardware implementation.

Main Methods:

• A compact memristor structure unit was utilized to construct the discrete chaotic system.
• A novel memristor-type chaotic mapping was mathematically designed and analyzed.
• System parameters were identified as partial and total amplitude controllers.
• Bifurcation analysis was performed to understand system dynamics.
• A hardware experiment using STM32 microcontroller verified the theoretical findings.

Main Results:

• A new memristor-type chaotic mapping was successfully designed.
• Two independent system parameters were confirmed as effective amplitude controllers.
• The internal memristor parameter was shown to induce typical bifurcation behavior.
• Hardware experiments validated the theoretical predictions of the chaotic mapping.

Conclusions:

• The developed memristor-type chaotic mapping represents a novel contribution to discrete chaotic systems.
• The system offers effective amplitude control and exhibits rich dynamical behavior.
• Hardware verification confirms the practical applicability of the proposed memristor-based chaotic system.