Design and application of multisroll conservative chaotic system with no-equilibrium, dynamics analysis, circuit implementation

Compared to dissipative chaotic systems (DCS), conservative chaotic systems (CCS) have the feature of zero-sum for the Lyapunov exponents, which holds unique research significance. This paper proposes a novel design method for a multiscroll conservative chaotic system (MSCCS). Firstly, a new cosine magneto-memristor is proposed. Then, based on the Sprott-A system, a new four-dimensional memristive conservative chaotic system (4D MCCS) is introduced. Finally, by introducing piecewise linear functions into the 4D MCCS, A one-directional multisroll conservative chaotic system (1D-MSCCS) and a two-directional multisroll conservative chaotic system (2D-MSCCS) are proposed. The dynamical analysis of the system shows that MSCCS has no-equilibrium points and possesses hidden attractors, belonging to the class of non-Hamiltonian conservative chaotic systems (non-HCCS), with larger Lyapunov exponents compared to other CCS. As parameters vary, the system exhibits various attractor structures. By introducing external bias, the system exhibits offset-boosting behavior. Under different numbers of initial conditions, the system displays dynamical phenomenon such as coexistence of attractors, multistability, and super multistability. Complexity analysis results demonstrate that the MSCCS has higher complexity compared with other CCS. The accuracy and practical existence for the MSCCS math model are tested by analog circuits. Additionally, MSCCS is implemented through digital circuits using the STM32 microcontroller. The article closes based on the MSCCS, a finite-time synchronization system with controllable synchronization time is designed. MSCCS can be applied in various fields such as communication security, random number generation, nonlinear control, chaos modulation, sensor networks, and embedded systems.