Abstract
This paper describes evolution of new active element that is able to significantly simplify the design process of lumped chaotic oscillator, especially if the concept of analog computer or state space description is adopted. The major advantage of the proposed active device lies in the incorporation of two fundamental mathematical operations into a single five-port voltage-input current-output element: namely, differentiation and multiplication. The developed active device is verified inside three different synthesis scenarios: circuitry realization of a third-order cyclically symmetrical vector field, hyperchaotic system based on the Lorenz equations and fourth- and fifth-order hyperjerk function. Mentioned cases represent complicated vector fields that cannot be implemented without the necessity of utilizing many active elements. The captured oscilloscope screenshots are compared with numerically integrated trajectories to demonstrate good agreement between theory and measurement.
Highlights
The synthesis and practical realization of chaotic deterministic dynamical systems in the form of lumped electronic circuits is an old and well-established problem
The very first concepts of the analog chaotic oscillators were designed to be simple and transparent, in order to demonstrate the fundamental nature of chaos and the conditions that are required for the evolution of chaotic behavior
This paper brings detailed description of the integrated bipolar/CMOS design of a new active element denoted-by-authors as Differential Voltage Trans-Conductance Multiplier (DV-TC-M) that is optimized from the viewpoint of circuit modeling of the smooth vector fields
Summary
The synthesis and practical realization of chaotic deterministic dynamical systems in the form of lumped electronic circuits is an old and well-established problem. The very first concepts of the analog chaotic oscillators were designed to be simple and transparent, in order to demonstrate the fundamental nature of chaos and the conditions that are required for the evolution of chaotic behavior. These circuits can be considered as a parallel connection of the higher-order admittance network and nonlinear active two-terminal device. Polynomial resistors with arbitrary degrees [3] can be connected in parallel with a third-order fully passive admittance network to obtain a robust chaotic oscillator [4,5] as well. Higher-order polynomial resistors can be used to approximate goniometric functions and connected as the fundamental nonlinearity inside suitable circuit topology to generate the so-called multiscroll [6,7,8] or multigrid strange attractors [9,10]
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