Four current-tunable chaotic oscillators in set of two diode-reversible pairs

Abstract

Four current-tunable chaotic oscillators are presented in a set of two diode-reversible pairs. The first pair employs a floating-diode technique whereas the second pair employs a virtually-grounded-diode technique. Two chaotic attractors of a pair are 1808-rotated images of each other. Each oscillator consists of six basic electronic components which are minimal in a category of chaotic oscillators that exploit a capacitorinductor-capacitor network, opamp(s), diode(s) and resistor(s). Current-tunable bifurcations are demonstrated.Introduction: Studies of chaotic circuits have attracted great attention owing to a variety of applications in science and technology, e.g. chaos-based secure communications [1,2]. Existing 3D chaotic oscillators include a category that employs six types of basic electronic components, i.e. a capacitor-inductor-capacitor (CLC) network, opamp(s), diode(s) and resistor(s). Such a category is of particular interest as most components, except the nonlinear diode, are linear building blocks commonly found in classical sinusoidal oscillators. Although six minimum numbers of components are desirable if each type is reduced to one component, most chaotic oscillators in this category have employed more than six components [3][4][5], but never been demonstrated clearly using a current-tunable technique. In this Letter, four current-tunable chaotic oscillators are presented in a set of two diodereversible pairs. Each oscillator consists of six minimal components in the category and is capable of current-tunable bifurcations.

A simple current-reversible chaotic jerk circuit using inherent tanh(x) of an opamp

“…For instance, the chaotic circuits that were early proposed based on a positive-feedback loop [4] and a biquadratic filter [5], a chaotic circuit based on a single opamp has employed a diode [6], whereas a chaotic jerk circuit based on two opamps has employed sgn(x) nonlinearity [7]. Recently, current-tunable chaotic circuits have been demonstrated for such a category using either exponential nonlinearity of a diode with a single opamp [8,9], or sgn(x) nonlinearity with two opamps [10]. Although the former has exploited a current source I 0 for a dynamical model [8] and a jerk model [9], I 0 has encountered difficulty in a reverse direction due to the diode direction.…”

“…Recently, current-tunable chaotic circuits have been demonstrated for such a category using either exponential nonlinearity of a diode with a single opamp [8,9], or sgn(x) nonlinearity with two opamps [10]. Although the former has exploited a current source I 0 for a dynamical model [8] and a jerk model [9], I 0 has encountered difficulty in a reverse direction due to the diode direction. Although the later [10] has exploited current-reversible I 0 without such difficulty, the two required opamps have resulted in a relatively complicated chaotic jerk circuit.…”

A new current-tunable chaotic jerk equation and a new homoclinic orbit of an existing minimal chaotic circuit

“…Recently, current-tunable circuits have been employed for both Group-I [6,7] and Group-II [3,4]. Four existing currenttunable chaotic circuits reported in [6] of Group-I have been of particular interest as each of them have been implemented using six minimum numbers of basic electronic components in the category of chaotic oscillators that employ a capacitorinductor-capacitor (CLC) network, op-amp(s), diode(s) and resistor(s).…”

“…Four existing currenttunable chaotic circuits reported in [6] of Group-I have been of particular interest as each of them have been implemented using six minimum numbers of basic electronic components in the category of chaotic oscillators that employ a capacitorinductor-capacitor (CLC) network, op-amp(s), diode(s) and resistor(s). Although each of the four circuits in [6] has been minimal in its category, a chaotic jerk equation of each circuit has never been found. It is natural to wonder whether the chaotic jerk equation is possible for such a minimal circuit.…”

Current‐tunable chaotic jerk circuit based on only one unity‐gain amplifier

“…Type-II has increasingly attracted much attention due to its simplicity [2,3]. Recently, current-tunable approaches have been reported for the type-I [4,5] and type-II [2]. In addition, techniques of unity-gain amplifiers have been exploited not only for sinusoidal oscillators [6,7], but also for chaotic oscillators of type-I.…”