New nonlinear active element dedicated to modeling chaotic dynamics with complex polynomial vector fields

New nonlinear active element dedicated to modeling chaotic dynamics with complex polynomial vector fields

Článek WoS

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.

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.

bifurcation diagram; chaotic oscillator; Lyapunov exponents; polynomial vector field; squarer; trans-conductance mode

bifurcation diagram; chaotic oscillator; Lyapunov exponents; polynomial vector field; squarer; trans-conductance mode

PETRŽELA, J.; ŠOTNER, R.

2020

06.09.2019

MDPI

Basel, Switzerland

1099-4300

Entropy

21

9

Švýcarská konfederace

1

37

37

https://www.mdpi.com/1099-4300/21/9/871

http://hdl.handle.net/11012/180645

entropy-21-00871