Antimonotonicity and chaotic dynamics in a fourth-order autonomous nonlinear electric circuit

I. M. Kyprianidis, I. N. Stouboulos, P. Haralabidis, T. Bountis

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

In this paper we study the dynamics of a fourth-order autonomous nonlinear electric circuit with two active elements, one linear negative conductance and one nonlinear resistor with a symmetrical piecewise-linear v-i characteristic. Using the capacitances C1 and C2 as the control parameters, we observe the phenomenon of antimonotonicity and the formation of "bubbles" in the development of bifurcations, resulting typically in reverse period-doubling sequences. We also find a crisis-induced intermittency, when the spiral attractor suddenly widens to a double-scroll attractor. We have plotted several bifurcation diagrams of reverse period-doubling sequences and computed the scaling parameter δ versus the control parameter C2 for the different regimes, where bubbles evolve. Thus, besides the usual Feigenbaum constant δ → δF = 4.6692 ..., we also observe, in some cases, a convergence of δ to √δF, as expected from theoretical considerations. Finally, by plotting a return map associated with one of the state variables, we demonstrate the strongly one-dimensional character of the dynamics and discuss the dependence of this map on the parameters of the system.

Original languageEnglish
Pages (from-to)1903-1915
Number of pages13
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume10
Issue number8
Publication statusPublished - Aug 2000
Externally publishedYes

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Period Doubling
Chaotic Dynamics
Control Parameter
Bubble
Fourth Order
Attractor
Reverse
Return Map
Networks (circuits)
Intermittency
Bifurcation Diagram
Capacitance
Conductance
Piecewise Linear
Resistors
Bifurcation
Scaling
Demonstrate
Character
Crisis

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

Antimonotonicity and chaotic dynamics in a fourth-order autonomous nonlinear electric circuit. / Kyprianidis, I. M.; Stouboulos, I. N.; Haralabidis, P.; Bountis, T.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 10, No. 8, 08.2000, p. 1903-1915.

Research output: Contribution to journalArticle

Kyprianidis, I. M. ; Stouboulos, I. N. ; Haralabidis, P. ; Bountis, T. / Antimonotonicity and chaotic dynamics in a fourth-order autonomous nonlinear electric circuit. In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2000 ; Vol. 10, No. 8. pp. 1903-1915.
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