Generation of Multi-Scroll Chaotic Attractors from a Jerk Circuit with a Special Form of a Sine Function

Abstract

A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are infinite equilibrium points in this system, the scroll number of the generated chaotic attractors is certain under appropriate system parameters. The dynamical properties of the proposed chaotic system are studied through Lyapunov exponents, phase portraits, and bifurcation diagrams. It is found that the scroll number of the chaotic system in the left and right part of the x-y plane can be determined arbitrarily by adjusting the values of the parameters in the SFSF, and the size of attractors is dominated by the frequency of the SFSF. Finally, an electronic circuit of the proposed chaotic system is implemented on Pspice, and the simulation results of electronic circuit are in agreement with the numerical ones.

Generation of 3-D Grid Multi-Scroll Chaotic Attractors Based on Sign Function and Sine Function

“…Hence, many researchers have studied the multi-scroll chaotic system with different directions, and reported large amounts of that with different dynamical characteristics. According to how many directions have generated scrolls, the multi-scroll chaotic system can be divided as one-directional (1-D) [14][15][16][17][18][19][20][21][22][23], two-directional (2-D) [17,[23][24][25][26], three-directional (3-D) [25][26][27][28][29][30][31], and so on. A 1-D multi-scroll chaotic attractors based on Chua's circuit are designed by Suykens [14].…”

“…Sánchez-López [17] using staircase functions designed 1-D and 2-D chaotic attractors, Zhang and Yu [18] used triangular wave, sawtooth wave and hysteresis sequence to realize 2-D chaotic attractors, respectively. A 1-D chaotic attractor is also designed based on a saturated nonlinear function [20], in addition, Ding et al [22] designed a 1-D chaotic attractor by using a special form of sine function. Günay et al [23] designed a 1-D and 2-D multi-scroll chaotic attractor via hyperbolic tangent function.…”

Generation multi-scroll chaotic attractors using composite sine function and its application in image encryption

“…( ) For generating multiple scrolls in chaotic system, many different types of sine functions are proposed, such as normal sine function h x ( ) [21,24,29], modulated sine function j x ( ) [22], mathematical expression changed sine function k x ( ) [19], s x ( ) [30] and t x ( ) [31,32]. These sine functions are represented as follows.…”

Sincronización de sistemas caóticos de múltiple enrollamiento mediante observador de estado extendido

“…Como se menciona anteriormente, este tipo de sistemas no contiene productos de sus variables de estado en el modelo, es decir, estos presentan una función no lineal que genera los enrollamientos. En la literatura se ha reportado modelos caóticos de múltiple enrollamiento con un término no lineal conformado por funciones lineales por partes (PWL, por su sigla en inglés "piecewise linear") (Carbajal-Gómez y Sánchez-López, 2019;Tlelo-Cuautle et al, 2015), por formas especiales de una función seno (SFSF, por su sigla en inglés special form of a sine function), funciones hiperbólicas (Chen et al, 2017;Signing et al, 2019), entre otras, (Ding y Feng, 2020;Li y Zeng, 2023).…”