A novel method for extending multi-scroll hidden attractors in multiple directions

Abstract Multi-scroll chaotic system exhibits unique dynamic characteristics and rich nonlinear performances, presenting broad application prospects in numerous fields such as signal processing and secure communication. In this paper, a nonlinear function with piecewise linear characteristics is introduced into an improved Chua’s system with a five-scroll hidden attractor, and new five-dimensional and six-dimensional multi-scroll chaotic systems are constructed. The added nonlinear function enables the new systems to generate 2 N +1 and 2 M +2 five-scroll hidden attractors in multiple directions on the phase plane. The mechanism underlying the expansion of five-scroll hidden attractors is investigated by MATLAB, revealing that the quantity of expansion depends on the number of intersections between the nonlinear function and the independent variable. Therefore, the quantity of the five-scroll hidden attractors in multiple directions can be conveniently adjusted through the internal core parameters of the nonlinear function. Interestingly, the investigation on the dynamical behaviors of the two newly constructed multi-scroll chaotic systems shows a phenomenon of initial-boosting behavior. Further analysis reveals that the new systems possess multistability and coexisting attractors, and the quantity of coexisting attractors is influenced jointly by the quantity of intersections between the nonlinear function and the independent variable as well as the initial values. Finally, the feasibility of these two new systems is verified on the Multisim 14.3 through a modular circuit design, and the results are consistent with the numerical simulation results obtained on the MATLAB.