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Published on: September 5, 2018
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A new four-dimensional chaotic system with rich transitional characteristics between dissipative and conservative
Xu Sun1, Xiangxin Leng2, Bowen Tian3
1Electronic Engineering College, Heilongjiang University, Harbin 150080, China.
Chaos (Woodbury, N.Y.)
|August 14, 2024
Summary
This study introduces a novel four-dimensional chaotic system with dual properties. Its fractional-order variant transitions from dissipative to conservative, exhibiting complex, pseudo-random chaotic sequences with hardware validation.
Area of Science:
- Nonlinear Dynamics and Chaos Theory
- Computational Physics
- Complex Systems
Background:
- Hamiltonian mechanics provides a fundamental framework for describing dynamical systems.
- Understanding chaotic systems is crucial for advancements in various scientific and engineering fields.
- Fractional-order systems offer unique dynamics compared to their integer-order counterparts.
Purpose of the Study:
- To develop a new four-dimensional chaotic system based on the general form of the Hamiltonian function.
- To investigate the influence of system parameters and initial values on the chaotic behavior.
- To propose and analyze a fractional-order version of the newly constructed chaotic system.
Main Methods:
- Formulation of a four-dimensional chaotic system using Hamiltonian principles.
- Analysis of parameter influence (external excitation 'd', internal 'a', initial values) on system dynamics.
- Derivation and analysis of the corresponding fractional-order chaotic system.
- Investigation of system properties including dissipative-to-conservative transitions, coexisting attractors, complexity, and pseudo-randomness using NIST tests.
- Hardware implementation using a Digital Signal Processing (DSP) platform.
Main Results:
- A novel four-dimensional Hamiltonian-based chaotic system was successfully constructed.
- System parameters and initial conditions were found to significantly influence its properties.
- The fractional-order system exhibits a transition from dissipative to conservative behavior as the order 'q' increases.
- Multiple coexisting attractors were observed, dependent on Hamiltonian energy.
- Complexity analysis confirmed a high degree of complexity.
- NIST testing validated the pseudo-randomness of the generated chaotic sequences.
- Physical realizability was confirmed through a DSP hardware platform.
Conclusions:
- The developed four-dimensional chaotic system and its fractional-order counterpart demonstrate rich and tunable dynamics.
- The system's dual dissipative-conservative nature and complex, pseudo-random outputs hold potential for applications in secure communications and signal processing.
- The validated hardware implementation confirms the practical feasibility of the proposed chaotic system.
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