Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication.

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Solid-State Electronics
• Information Security

Background:

• Continuous-time memristors are prevalent in chaotic circuits, but discrete-time memristor models are underexplored.
• One-dimensional chaotic systems suffer from short periods and uneven output distribution, limiting their practical applications.
• The TiO2 memristor model is a key component in memristive systems.

Purpose of the Study:

• To discretize the TiO2 memristor model using the backward-Euler method.
• To enhance the dynamic characteristics of one-dimensional chaotic systems.
• To develop a novel two-dimensional discrete-time memristor model for improved chaotic behavior.

Main Methods:

• Discretization of the TiO2 memristor model via the backward-Euler method.
• Linear coupling of the discrete TiO2 memristor model with one-dimensional chaotic systems.
• Analysis of the stability of infinite fixed points in the two-dimensional model based on coupling parameters and initial states.

Main Results:

• The discretized TiO2 memristor model satisfies the generalized memristor characteristics.
• A two-dimensional discrete-time memristor model with enhanced chaotic dynamics was successfully developed.
• The stability of the model's fixed points was shown to be dependent on coupling parameters and initial conditions.

Conclusions:

• The proposed discrete-time memristor model effectively enhances chaotic system dynamics.
• The developed two-dimensional model offers potential for generating improved chaotic sequences.
• The generated chaotic sequences are applicable to secure communication systems.