Dynamic analysis and geometric control of a novel parametrically controllable multi-scroll conservative chaotic system

This paper presents a novel parametrically controllable multi-scroll conservative chaotic system with a concise mathematical model and rich dynamic properties. The number of scrolls in the chaotic system can be regulated by a single control parameter c. Numerical simulations and theoretical analyses were performed to verify the conservative and hidden properties of the proposed system in terms of Lyapunov exponent, Equilibrium points, Kaplan–Yorke dimension. In addition, several interesting dynamical phenomena are found here, including the hidden extreme multistability, a special offset boosting and similar transient behaviors. To increase the diversity and complexity of the system, we propose a universal cascade control model with the purpose of achieving geometric control of digitized chaotic systems. The proposed scheme can flexibly and effectively control chaotic phase diagrams in 3-D space by changing the forward and reverse regulation matrices of the cascade control model. Finally, a microcontroller-based platform was built to implement the proposed 3-D system. The novel multi-scroll conservative chaotic system has rich and peculiar dynamics and is suitable for application in chaotic secure communication.