Chaotic and Hyperchaotic Self-Oscillations of Lambda Diode Composed by Generalized Bipolar Transistors

Jiri Petrzela

doi:10.3390/app11083326

Abstract

This paper is focused on the investigation of self-oscillation regimes associated with very simple structure of lambda diode. This building block is constructed by using coupled generalized bipolar transistors. In the stage of mathematical modeling, each transistor is considered as two-port described by full admittance matrix with scalar polynomial forward trans-conductance and linear backward trans-conductance. Thorough numerical analysis including routines of dynamical flow quantification indicate the existence of self-excited dense strange attractors. Plots showing first two Lyapunov exponents as functions of adjustable parameters, signal entropy calculated from generated time sequence, sensitivity analysis, and other results are provided in this paper. By the construction of a flow-equivalent chaotic oscillator, robustness and long-time geometrical stability of the generated chaotic attractors is documented by the experimental measurement, namely by showing captured oscilloscope screenshots.

Highlights

After discovery of first and very simple fully analog chaotic system, famous Chua’s oscillator, both theoretical and practical significance of research focused on the nonlinear dynamics and chaos theory has been recognized immediately
After discovery of iconic Chua’s circuit, in nearly four subsequent decades, many chaotic dynamical systems were discovered; either accidentally, during numerical investigation of mathematical model associated with real physical phenomenon, or by using numerical algorithms dedicated for chaos localization
This paper presents thorough numerical analysis of a new hyperchaotic dynamical system and shows its robust fully analog circuitry realization

Summary

Introduction

After discovery of iconic Chua’s circuit, in nearly four subsequent decades, many chaotic dynamical systems were discovered; either accidentally, during numerical investigation of mathematical model associated with real physical phenomenon, or by using numerical algorithms dedicated for chaos localization. For the latter case, fitness function could be considered as topology of evolved state attractors [6], set of one-dimensional

Methods

Discussion

Conclusion