Abstract
A five-dimensional (5D) controlled two-stage Colpitts oscillator is introduced and analyzed. This new electronic oscillator is constructed by considering the well-known two-stage Colpitts oscillator with two further elements (coupled inductors and variable resistor). In contrast to current approaches based on piecewise linear (PWL) model, we propose a smooth mathematical model (with exponential nonlinearity) to investigate the dynamics of the oscillator. Several issues, such as the basic dynamical behaviour, bifurcation diagrams, Lyapunov exponents, and frequency spectra of the oscillator, are investigated theoretically and numerically by varying a single control resistor. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling and interior crisis routes as the single control resistor is monitored. Furthermore, an experimental study of controlled Colpitts oscillator is carried out. An appropriate electronic circuit is proposed for the investigations of the complex dynamics behaviour of the system. A very good qualitative agreement is obtained between the theoretical/numerical and experimental results.
Highlights
During the last three decades, a tremendous attention has been devoted to design chaotic electronic oscillators
In contrast to current approaches based on piecewise linear (PWL) model, we propose a smooth mathematical model to investigate the dynamics of the oscillator
This paper has introduced and investigated the dynamics of the new controlled two-stage Colpitts oscillator
Summary
During the last three decades, a tremendous attention has been devoted to design chaotic electronic oscillators The focus on this interesting research field comes mainly from two facts: first, one can observe chaos and can control the dynamics of the oscillator by changing the physically accessible parameters of the oscillator, for example, linear resistor, linear capacitor, voltage levels, coupled inductors, and so forth; second, there are a multitude of applications of chaotic electronic oscillators starting from chaotic electronic secure communication to cryptography [1]. The effects of transistor gain on the dynamics of the controlled two-stage Colpitts oscillator are analyzed
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