A Novel Megastable Oscillator with a Strange Structure of Coexisting Attractors: Design, Analysis, and FPGA Implementation

Kui Zhang,Karthikeyan Rajagopal,Iqtadar Hussain,Hayder Natiq,Sajad Jafari,M D Vijayakumar,Sajjad Shaukat Jamal,Ahmed A Abd El-Latif

doi:10.1155/2021/2594965

Abstract

Megastable chaotic systems are somehow the newest in the family of special chaotic systems. In this paper, a new megastable two-dimensional system is proposed. In this system, coexisting attractors are in some islands, interestingly covered by megalimit cycles. The introduced two-dimensional system has no defined equilibrium point. However, it seems that the origin plays the role of an unstable equilibrium point. Therefore, the attractors are determined as hidden attractors. Adding a forcing term to the system, we can obtain chaotic solutions and coexisting strange attractors. Moreover, the effect of three different values of the forcing term’s amplitude is studied. The dynamical properties of the designed system are investigated using attractor plots, bifurcation diagrams, and Lyapunov Exponents diagram. Phase portraits of the novel megastable oscillator are presented by FPGA design. Xilinx system generator block diagrams of the proposed system and trigonometric functions are also presented.

Highlights

Finding new special chaotic systems or, new systems with special and unique dynamical characteristics has been an active area of research since about 30 years ago
It was believed that the strange attractors and unstable equilibrium points have a strong relationship
No equilibrium point was found for the proposed two-dimensional system

Summary

A Novel Megastable Oscillator with a Strange Structure of Coexisting Attractors

A new megastable two-dimensional system is proposed. In this system, coexisting attractors are in some islands, interestingly covered by megalimit cycles. E introduced two-dimensional system has no defined equilibrium point. It seems that the origin plays the role of an unstable equilibrium point. Adding a forcing term to the system, we can obtain chaotic solutions and coexisting strange attractors. Phase portraits of the novel megastable oscillator are presented by FPGA design. Xilinx system generator block diagrams of the proposed system and trigonometric functions are presented

Introduction

A New Megastable Chaotic Oscillator

FPGA Implementation of Novel Megastable Oscillator

Conclusion