Bifurcation analysis and circuit simulation of a novel four-scroll dynamical system with multistability and amplitude control

Abstract This paper introduces a multistable four-scroll 3D chaotic system with amplitude control, offering a significant enhancement to the traditional four-scroll systems by allowing for dynamic adjustment of the amplitude of the chaotic oscillations. The system’s dynamics are thoroughly analyzed using equilibrium point analysis, Lyapunov exponents, bifurcation diagrams, and basins of attraction, revealing the presence of multiple stable attractors under different parameter configurations. The incorporation of amplitude control adds a new layer of flexibility, enabling the system to switch between different attractor states, including the four-scroll chaotic attractors, in a controlled manner. This multistable behavior with amplitude control is particularly valuable for applications in secure communication, chaos-based cryptography, and nonlinear signal processing. Moreover, transient chaotic behavior often emerges at certain parameter values where the system transitions between different dynamical regimes, highlighting the delicate balance between stability and chaos. An electronic circuit simulation is designed and implemented to validate the theoretical findings. The experimental results show that the circuit closely replicates the chaotic dynamics predicted by the mathematical model, including the successful realization of four-scroll chaotic attractors. The proposed system provides a promising framework for designing versatile chaotic systems with potential applications in diverse fields that require precise control over chaotic behavior.