Memcapacitor model and its application in chaotic oscillator with memristor

Area of Science:

• Nonlinear Dynamics and Circuit Theory
• Advanced Electronic Components

Background:

• Memristors and memcapacitors are emerging nonlinear circuit elements exhibiting memory properties.
• Understanding their behavior in complex circuits is crucial for developing new electronic functionalities.

Purpose of the Study:

• To design and analyze a novel chaotic oscillator incorporating Hewlett-Packard memristor and charge-controlled memcapacitor models.
• To explore the complex dynamical behaviors and characteristics of these memory elements within nonlinear circuits.

Main Methods:

• Theoretical and numerical investigation of the oscillator's equilibrium sets, Lyapunov exponent spectrums, and bifurcations.
• Development of a discrete model for the chaotic oscillator.
• Experimental verification using Digital Signal Processing (DSP) chips and National Institute of Standards and Technology (NIST) tests.

Main Results:

• The proposed oscillator exhibits complex dynamics, including an infinite number of equilibria, coexisting oscillations, and multi-stability.
• The study provides a comprehensive analysis of the oscillator's fundamental dynamical behaviors.
• Experimental validation confirms the main statistical properties of the designed chaotic oscillator.

Conclusions:

• The novel chaotic oscillator effectively demonstrates the complex dynamics of memristors and memcapacitors in nonlinear circuits.
• The findings contribute to a deeper understanding of memory elements in advanced electronic systems.
• Experimental verification validates the theoretical models and the oscillator's behavior.