Didactic model of a simple driven microwave resonant T-L circuit for chaos, multistability and antimonotonicity

Abstract

A simple driven bipolar junction transistor (BJT) based two-component circuit is presented, to be used as didactic tool by Lecturers, seeking to introduce some elements of complex dynamics to undergraduate and graduate students, using familiar electronic components to avoid the traditional black-box consideration of active elements. Although the effect of the base-emitter (BE) junction is practically suppressed in the model, chaotic phenomena are detected in the circuit at high frequencies (HF), due to both the reactant behavior of the second component, a coil, and to the birth of parasitic capacitances as well as to the effect of the weak nonlinearity from the base-collector (BC) junction of the BJT, which is otherwise always neglected to the favor of the predominant but now suppressed base-emitter one. The behavior of the circuit is analyzed in terms of stability, phase space, time series and bifurcation diagrams, Lyapunov exponents, as well as frequency spectra and Poincaré map section. We find that a limit cycle attractor widens to chaotic attractors through the splitting and the inverse splitting of periods known as antimonotonicity. Coexisting bifurcations confirm the existence of multi-stability behaviors, marked by the simultaneous apparition of different attractors (periodic and chaotic ones) for the same values of system parameters and different initial conditions. This contribution provides an enriching complement in the dynamics of simple chaotic circuits functioning at high frequencies. Experimental lab results are completed with PSpice simulations and theoretical ones.

Logistic Curve Modeling of the Germination of Beans Seeds Phaseolus Vulgaris Previously Exposed to Multi-Periodic and Chaotic Electromagnetic Fields

“…These authors used an electronic circuit of a few components Tchitnga [23] out of a family of simple chaotic circuits comprising a coil Tchitnga Talla & Zebaze Nanfa'a [24][25][26] to generate electromagnetic signals of various periods (period-1, period-2, period-4) as well as a chaotic signal. These various signals were applied to the bean plants during their evolution 24 hours a day and 7 days a week.…”

FPGA Implementation of a Novel Two-internal-State Memristor and its Two Component Chaotic Circuit

“…The circuit is modeled in a three differential equation system and shows complicated dynamics. Many more strives have been made of recent in an effort to simplify chaotic systems in terms the number of elements used in the circuit (10)(11)(12) . Recently, researchers are using not just the properties of memristors, but memory devices (memdevices) to reduce the number of elements in a circuit that are required for chaotic oscillations (13) .…”

Non periodic oscillations, bistability, coexistence of chaos and hyperchaos in the simplest resistorless Op-Amp based Colpitts oscillator

“…In the frame work of the present paper, we aim at showing that as a real physically two-component circuit made of a field effect transistor and a tapped coil has led to chaos [17], it is also possible, under particular attention, to find coexistence of chaos and hyperchaos in a real physically four-component autonomous circuit which on one hand can be used as simple didactic model [18,19,20]. At the same time, on the other hand, it fits into engineering systems with applications based on chaos and hyperchaos, and can therefore be used in secure communication [1,2,11,21,22], in pseudo and true random bit generation [23,24], for the study of complex bifurcations [25,26], as well as for the simulation of collective motion of huge group of individuals such as flock of birds [27], just to name some.…”