A chaotic circuit under a new classification framework of inductorless Chua’s circuits

Abstract

Purpose This paper aims to classify the inductorless Chua’s circuits into two types from the topological structures and construct a chaotic circuit under this new classification framework. Design/methodology/approach In this paper, two types of inductorless Chua’s circuit models are presented from topological structure, among which the first type of inductorless Chua’s circuit (FTICC) model is much closer to the original Chua’s circuit. Under this classification framework, a new inductorless Chua’s circuit that belongs to the FTICC model is built by replacing LC parallel resonance of the original Chua’s circuit with a second order Sallen–Key band pass filter. Findings Compared with a paradigm of a reported inductorless Chua’s circuit that belongs to the second type of inductorless Chua’s circuit (STICC) model, the newly proposed circuit can present the attractors which are much more closely to the original Chua’s attractors. The dynamical behaviors of coexisting period-doubling bifurcation patterns and boundary crisis are discovered in the newly proposed circuit from both numerical simulations and experimental measurements. Moreover, a crisis scenario is observed that unmixed pairs of symmetric coexisting limit cycles with period-3 traverse through the entire parameter interval between coexisting single-scroll chaotic attractors and double-scroll chaotic attractor. Originality/value The newly constructed circuit enriches the family of inductorless Chua’s circuits, and its simple topology with small printed circuit board size facilitates the various types of engineering applications based on chaos.

Coexisting Attractors in a New Smooth Inductorless Chua’s Circuit

“…Here the partial circuit on the left of port 22' is a second order Sallen-Key band pass filter (BPF) [3], and the partial circuit between port 11' and 22' is a resistance capacitance coupled network, and the partial circuit on the right of port 11' is a smooth Chua's diode formed by active diode pair [4]. According to the classification framework of inductorless Chua's circuits proposed in [2], this new circuit belongs to the FTICC model [2].…”

“…Because of the troubles for making and applying inductance, various inductorless Chua's circuits get a lot of attention by researchers. In [2], inductorless Chua's circuits are divided into two categories from the similarity to the traditional Chua's circuit. In this article, a new inductorless Chua's circuit that belongs to the model of FTICC [2] is presented based on a second order Sallen-Key BPF.…”

“…In [2], inductorless Chua's circuits are divided into two categories from the similarity to the traditional Chua's circuit. In this article, a new inductorless Chua's circuit that belongs to the model of FTICC [2] is presented based on a second order Sallen-Key BPF. Unlike the inductorless Chua's circuit in [2], an active diode pair [4] is introduced in the new circuit as a Chua's diode.…”

“…In this article, a new inductorless Chua's circuit that belongs to the model of FTICC [2] is presented based on a second order Sallen-Key BPF. Unlike the inductorless Chua's circuit in [2], an active diode pair [4] is introduced in the new circuit as a Chua's diode. Because of the hyperbolic sine nonlinearity in active diode pair, the new circuit is smooth, not piecewise-linear.…”

Coexisting Multiple Attractors in a Fourth Order Chua’s Circuit With Experimental Verifications by Analog and Digital Circuits

“…As a study focus among the nonlinear circuits, the classical third order Chua's circuit [9], [10] demonstrates the chaos phenomenon perfectly in theory and practice [11], [12]. On the basis of this classical circuit, the various forms of generalized Chua's circuits and systems [13]- [26] build a deep recognition of chaos for the academia further. In these studies, the new features such as stable equilibrium points [14]- [17], multi-scroll attractors [18]- [21], multiple attractors [17], multiple scroll coexisting attractors [22], SC-CNN-based mode [23] and inductorless implementation approaches [24]- [26] have been revealed in succession.…”