Parameter Identification of Fractional-Order Discrete Chaotic Systems

Area of Science:

• Chaos theory
• Nonlinear dynamics
• Computational mathematics

Background:

• Fractional-order discrete chaotic systems are a growing research area.
• Chaos synchronization in these systems is a novel and challenging topic.
• Existing synchronization methods have limitations.

Purpose of the Study:

• To propose an improved particle swarm optimization (PSO) algorithm for parameter identification in fractional-order discrete chaotic systems.
• To address deficiencies in current chaos synchronization techniques.
• To determine optimal sample sizes and assess performance under noise.

Main Methods:

• Development of an improved particle swarm optimization (PSO) algorithm.
• Numerical simulations using Hénon map, Cat map, and fractional-order iterated maps.
• Analysis of parameter identification with varying sample sizes and noise interference.

Main Results:

• The proposed improved PSO algorithm demonstrated superior performance compared to six existing algorithms.
• The algorithm proved effective even in the presence of random noise interference.
• Optimal sample size analysis indicated two samples are most efficient for fractional-order systems, while integer-order systems require only one.

Conclusions:

• The improved PSO algorithm is a highly effective tool for parameter identification in fractional-order discrete chaotic systems.
• The study provides insights into sample size selection for efficient chaos synchronization.
• The method's robustness to noise is a significant advantage for practical applications.