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Dynamics and Entropy Analysis for a New 4-D Hyperchaotic System with Coexisting Hidden Attractors
Licai Liu1, Chuanhong Du1, Xiefu Zhang2
1School of Electronic and Information Engineering, Anshun University, Anshun 561000, China.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Researchers developed a novel 4-D hyperchaotic system exhibiting multistability and coexisting hidden attractors. This system generates diverse nonlinear dynamics, including chaotic and hyperchaotic behaviors, with potential applications in secure communications.
Area of Science:
- Nonlinear Dynamics and Chaos Theory
- Complex Systems Analysis
- Electrical Engineering and Circuit Design
Background:
- Multistable systems with coexisting hidden attractors are crucial for advanced applications.
- Understanding the complex dynamics of such systems remains a significant challenge.
- Existing models often lack the rich dynamical behaviors observed in real-world phenomena.
Purpose of the Study:
- To introduce a new no-equilibrium 4-D hyperchaotic multistable system.
- To explore the generation of diverse nonlinear complex attractors (periodic, quasiperiodic, chaotic, hyperchaotic).
- To investigate the physical realizability of the proposed chaotic system.
Main Methods:
- Analysis of system dynamics using Lyapunov exponents (LEs).
- Bifurcation analysis and Poincaré maps for characterizing system behavior.
- Spectral entropy (SE) for quantifying dynamical complexity.
- Circuit design and simulation for experimental verification.
Main Results:
- The proposed system exhibits a wide range of nonlinear complex attractors, including hidden attractors.
- Varying system parameters or initial conditions leads to diverse dynamical states.
- Lyapunov exponents, bifurcation diagrams, Poincaré maps, and spectral entropy confirm the system's hyperchaotic and multistable nature.
- Circuit design validates the physical feasibility of the proposed system.
Conclusions:
- The novel 4-D hyperchaotic multistable system demonstrates rich and complex hidden dynamic characteristics.
- The findings offer new insights into the behavior of systems with coexisting hidden attractors.
- The system presents a promising candidate for applications in nonlinear control and chaotic secure communication.
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