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

Abstract

A new current-tunable chaotic jerk circuit is proposed based on a single unity-gain amplifier. The circuit initially demonstrates a feasible use of a simple unity-gain amplifier for a chaotic jerk oscillator. Bifurcation is adjustable using a current source. Chaotic attractors are illustrated on an [X,Ẋ ] plane and an [ f 1 (X , Ẋ, Ẍ), Ẋ] plane. The latter is revealed numerically and experimentally where f 1 (X , Ẋ, Ẍ) is a simple algebraic sum of scaled X , Ẋ and Ẍ. A homoclinic orbit is included.

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

“…chaos-based secure communications [1,2]. Available threedimensional (3D) chaotic circuits may be isolated into two groups [3,4]. Group-I includes 3D chaotic oscillators represented by a set of three coupled first-order differential equations with three state variables such as the Chua's 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).…”

“…It is natural to wonder whether the chaotic jerk equation is possible for such a minimal circuit. In addition, a homoclinic orbit [4,7] of each of the four circuits in [6] has never been identified.…”