Minimal realizations of autonomous chaotic oscillators based on trans-immittance filters

Minimal realizations of autonomous chaotic oscillators based on trans-immittance filters

WoS Article

This review paper describes a design process toward fully analog realizations of chaotic dynamics that can be considered canonical (minimum number of the circuit elements), robust (exhibit structurally stable strange attractors), and novel. Each autonomous chaotic lumped circuit proposed in this paper can be understood as a looped system, where linear trans-immittance frequency lter interacts with an active nonlinear two-port. The existence of chaos is demonstrated via well-established numerical algorithms that represent the current standard in the eld of nonlinear dynamics, i.e., by calculation of the largest Lyapunov exponent and high-resolution 1-D bifurcation diagrams. The achieved numerical results are put into the context of experimental measurement; observed state trajectories prove a one-to-one correspondence between theoretical expectations and practical outputs, i.e., prescribed strange attractors do not represent the chaotic transients. Finally, short term unpredictability of the chaotic ow is demonstrated via calculation of KaplanYorke dimension that is high, i.e., generated waveforms can nd interesting applications in the elds of chaotic masking, modulation, or chaos-based cryptography.

This review paper describes a design process toward fully analog realizations of chaotic dynamics that can be considered canonical (minimum number of the circuit elements), robust (exhibit structurally stable strange attractors), and novel. Each autonomous chaotic lumped circuit proposed in this paper can be understood as a looped system, where linear trans-immittance frequency lter interacts with an active nonlinear two-port. The existence of chaos is demonstrated via well-established numerical algorithms that represent the current standard in the eld of nonlinear dynamics, i.e., by calculation of the largest Lyapunov exponent and high-resolution 1-D bifurcation diagrams. The achieved numerical results are put into the context of experimental measurement; observed state trajectories prove a one-to-one correspondence between theoretical expectations and practical outputs, i.e., prescribed strange attractors do not represent the chaotic transients. Finally, short term unpredictability of the chaotic ow is demonstrated via calculation of KaplanYorke dimension that is high, i.e., generated waveforms can nd interesting applications in the elds of chaotic masking, modulation, or chaos-based cryptography.

Analog oscillator, ltering two-port, chaos, immittance function, Lyapunov exponents, nonlinear dynamics, strange attractors

Analog oscillator, ltering two-port, chaos, immittance function, Lyapunov exponents, nonlinear dynamics, strange attractors

PETRŽELA, J.; POLÁK, L.

2019

31.01.2019

IEEE

USA

2169-3536

IEEE Access

7

1

United States of America

17561

17577

17

https://ieeexplore.ieee.org/document/8630955

08630955