Publication detail

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

PETRŽELA, J. ŠOTNER, R.

Original Title

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

English Title

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

Type

journal article - other

Language

en

Original 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.

English 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.

Keywords

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

Released

06.09.2019

Publisher

MDPI

Location

Basel, Switzerland

Pages from

1

Pages to

38

Pages count

38

URL

Full text in the Digital Library

BibTex


@article{BUT158448,
  author="Jiří {Petržela} and Roman {Šotner}",
  title="New nonlinear active element dedicated to modeling chaotic dynamics with complex polynomial vector fields",
  annote="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.",
  address="MDPI",
  chapter="158448",
  doi="10.3390/e21090871",
  howpublished="online",
  institution="MDPI",
  number="9",
  volume="21",
  year="2019",
  month="september",
  pages="1--38",
  publisher="MDPI",
  type="journal article - other"
}