Generation of n-scroll attractors via sine function

Abstract

A new approach for generating-scroll attractors is introduced. It is demonstrated that-scroll attractors can be generated using a simple sine or cosine function. A guideline is given so that a different number of scrolls can be designed easily by modifying two variables in the function. An electronic circuit is also designed for the implementation and the observation of a 9-scroll attractor is reported for the first time.

A 3-D four-wing attractor and its analysis

“…In [4,5,7], the piecewise-linear (PWL) function method was utilized, which can increase the number of equilibria by adding breakpoints. A sine-function approach was then proposed for creating multi-scroll chaotic attractors [8]. Later, a stair function was used for generating 3D-grid-scroll attractors [9,10].…”

A Brief Overview of Multi-Scroll Chaotic Attractors Generation

“…Tang et al [7] also constructed an electronic circuit to experimental verify these n−scroll chaotic attractors.…”

“…Tang et al [7] applied the sine function to replace the nonlinear characteristic function of Chua's circuit and obtained a modified Chua's circuit as follows:…”

“…Yalcin et al [6] experimentally confirmed the 3− and 5−scroll chaotic attractors in a generalized Chua's circuit. Tang et al [7][8] introduced a sine function to generate n−scroll attractors in a simple circuit with physically realizing up to a 10−scroll chaotic attractor observed on the oscilloscope. Similarly,Özoǧuz et al [3] suggested a nonlinear transconductor method for creating n−scroll chaotic attractors.…”

“…Multi-scroll chaotic attractors generation has become a relatively mature research direction today, after rapid developments in the last two decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”