Abstract
A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a modified sine function (MSF). In addition, the scrolls in Y and Z directions are generated by the sign function series, which are the superposition of some sign functions with different time-shift values. In the X-direction, the scroll number is adjusted by changing the comparative voltages of the MSF, and the ones in Y and Z directions are regulated by the sign function. The basic dynamics of Lyapunov exponent spectrum, phase diagrams, bifurcation diagram and equilibrium points distribution were studied. Furthermore, the circuits of the chaotic system are designed by Multisim10, and the circuit simulation results indicate the feasibility of the proposed chaotic system for generating chaotic attractors. On the basis of the circuit simulations, the hardware circuits of the system are designed for experimental verification. The experimental results match with the circuit simulation results, this powerfully proves the correctness and feasibility of the proposed system for generating 3-D grid multi-scroll chaotic attractors.
Highlights
Chaotic system with slight changing of initial value will produce different trajectories, and the power spectrum of chaotic system state variables is similar to random signals, the chaotic system has been widely studied around the world
X-direction is regulated by modified sine function (MSF), while the scroll number in Y-direction and Z-direction are controlled by sign function series
The n-scroll attractor in the X-direction is regulated by the modified sine function of f3 (x), while the m-scroll attractor in Y-direction and the p-scroll attractor in Z-direction are adjusted by f1 ( y) and f2 (z), respectively
Summary
Chaotic system with slight changing of initial value will produce different trajectories, and the power spectrum of chaotic system state variables is similar to random signals, the chaotic system has been widely studied around the world. The number of scrolls and the direction of scrolls affect the complexity of dynamic behavior of chaotic systems. Jia et al [33] studied a 1-D multi-scroll chaotic attractor based on Chua’s circuit with a nonlinearity of logarithmic function. Yu et al [36] used a modulating sine function as the nonlinearity in a general jerk system, and given 4-scroll and 8-scroll nesting chaotic attractors. Wu et al [42] presented a novel and simple 3-dimensional system with two sine functions that can generate abundant coexisting multiple attractors, but not a grid multi-scroll chaotic attractor. As far as we know, there is no 3-dimensional chaotic system with nonlinearity of the sine function for generating 3-D chaotic attractor, so design a sine function based 3-D grid multi-scroll chaotic attractor is a challenging task. X-direction is regulated by MSF, while the scroll number in Y-direction and Z-direction are controlled by sign function series
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