Chaos in a Single Op-Amp–Based Jerk Circuit: Experiments and Simulations

Abstract

We report a five-component autonomous chaotic oscillator of jerky type, hitherto the simplest of its kind, using only one operational amplifier. The key component of the circuit is a junction field-effect transistor operating in its triode region, which provides a nonlinear resistor of antisymmetrical current-voltage characteristic, emulating a Colpitts-like chaotic circuit. We describe the experimental results illustrating the dynamical behavior of the circuit. In addition, we report numerical simulations of a model of the circuit which display good agreement with our measurements.

A minimum five‐component five‐term single‐nonlinearity chaotic jerk circuit based on a twin‐jerk single‐op‐amp technique

“…The first advantage is much better than that of the simplest chaotic flow, whose circuit implementation will inevitably require more than 5 electronic components. Not only are the second and third advantages remarkably comparable to the simplest chaotic flow, but they also circumvent the 2 existing disadvantages in Tchitnga et al…”

“…On the other hand, circuit I in Figure A appears to be a slightly modified version of the existing 6‐term 2‐nonlinearity circuit in Tchitnga et al, ie, the gate of the JFET of circuit I is connected to node m , as shown in Figure A, whereas the gate of the JFET of Tchitnga et al, was differently connected to node n of Figure A, (the connection is not shown here). Although such a modification does not significantly alter the state equations of circuit I from those of the existing 6‐term 2‐nonlinearity circuit of Tchitnga et al, it allows circuits I and II to form mirrored images of each other. The term “mirrored” is used in the sense that the 2 positions of L and J of circuits I and II are symmetrically flipped positions to each other around the capacitor C 1 .…”

“…In the category that a single op‐amp is employed, 3D chaotic circuits with 6 electronic components have been reported, eg, Mumuangsaen and Srisuchinwong, whereas 3D chaotic jerk circuits have more than 6 components, eg, Sprott, Srisuchinwong and Treetanakorn, and Srisuchinwong and Nopchinda . Recently, a 5‐component 6‐term 2‐nonlinearity chaotic jerk circuit based on a single op‐amp has been reported . Two disadvantages of Tchitnga et al however remain in its set of 3 coupled first‐order ODEs, ie, ( 1 ) there are 6 algebraic terms which are not 5 minimum terms, and ( 2 ) there are 2 terms of nonlinearity in the ODEs, although a single passive nonlinear electronic component is used in the circuit.…”

“…The proposed minimum 5‐term single‐nonlinearity circuit and a slightly modified version of the existing 6‐term 2‐nonlinearity circuit in Tchitnga et al form mirrored images of each other. Although both mirrored circuits result in 2 different sets of 3 coupled first‐order ODEs, both sets can be transformed into a pair of twin jerk equations.…”

Secure color image encryption algorithm based on chaotic signals and its FPGA realization

“…And, we also discuss the construction of the chaotic system. Due to its potentiality, chaos has been applied in a lot of applications, for example, in liquid mixers, 22 nonlinear circuits, 23 and especially in secure communication. The first chaotic system was found by Lorenz in his studies on meteorology.…”