A Novel 2D – Grid of Scroll Chaotic Attractor Generated by CNN

Ahmed M Ali,Saif M Ramadhan,Fadhil R Tahir

doi:10.3390/sym11010099

Abstract

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line x=y has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array (1×3) cells. The paper concerns on the design and implementation of 2×2 and 3×3 2D-grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice.

Highlights

Since the treasure trove of Chua’s circuit [1], many scientists from different fields have been studying the double scroll attractors
Chua’s circuit is a paradigm for chaos, which in turn is deformed from 3D system
Many bifurcation phenomena have been described in [2], such as Hopf bifurcation, Rossler’s spiral, double scroll, etc., all these special emphases lead to the double scroll attractor

Summary

Introduction

Since the treasure trove of Chua’s circuit [1], many scientists from different fields have been studying the double scroll attractors. Chua’s circuit is a paradigm for chaos, which in turn is deformed from 3D system. Chua and Lui-nian Lin in [3], presented a canonical circuit capable of realizing every member of Chua’s family using a three-region system. The implementation of a smooth nonlinearity with a cubic polynomial or higher order was presented in [5], to overcome some subtle features of a real circuit. In [6], Xiao Fan and Guanrong Chen designed a linear feedback controller composed with nonlinear modulo or sawtooth function to drive the original nonlinear autonomous system.

Methods

Results

Conclusion