A New Megastable Chaotic Oscillator with Blinking Oscillation terms

Dhinakaran Veeman,Karthikeyan Rajagopal,Nadia M G Al-Saidi,Hayder Natiq,Sajad Jafari,Iqtadar Hussain,Jorge-Antonio Lopez-Renteria

doi:10.1155/2021/5518633

Abstract

Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, the existence of different coexisting attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated.

Highlights

Research ArticleMegastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems
Simple and elegant oscillators are interesting for researchers in the fields of nonlinear dynamics [1]
An equilibrium point in the basin of attraction is considered an important feature for chaotic attractors [3]. erefore, attractors can be classified into two main groups based on this feature: self-excited attractors and hidden attractors [4]

Summary

Research Article

Megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. The oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. E forced system can generate an infinitive number of hidden attractors without changing parameters. E behavior of these hidden attractors can be chaotic, tori, and limit cycle. The existence of different coexisting attractors with different kinds of behaviors reflects the system’s high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. The circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated

Introduction

LEs xmax

Complexity ymax

Conclusion