Asymmetric Double Strange Attractors in a Simple Autonomous Jerk Circuit

Abstract

The dynamics of a simple autonomous jerk circuit previously introduced by Sprott in 2011 are investigated. In this paper, the model is described by a three-time continuous dimensional autonomous system with an exponential nonlinearity. Using standard nonlinear techniques such as time series, bifurcation diagrams, Lyapunov exponent plots, and Poincaré sections, the dynamics of the system are characterized with respect to its parameters. Period-doubling bifurcations, periodic windows, and coexisting bifurcations are reported. As a major result of this work, it is found that the system experiences the unusual phenomenon of asymmetric bistability marked by the presence of two different attractors (e.g., screw-like Shilnikov attractor with a spiralling-like Feigenbaum attractor) for the same parameters setting, depending solely on the choice of initial states. Among few cases of lower dimensional systems capable of such type of behavior reported to date (e.g., Colpitts oscillator, Newton-Leipnik system, and hyperchaotic oscillator with gyrators), the jerk circuit/system considered in this work represents the simplest prototype. Results of theoretical analysis are perfectly reproduced by laboratory experimental measurements.

Symmetrically scaled coexisting behaviors in two types of simple jerk circuits

“…The Type 2 circuits shown in Figure 1(b) are achieved by unifying the autonomous jerk circuits dividually reported by Kengne et al (2016), Kom et al (2018) and Sprott (2011), whereas the Type 1 circuits shown in Figure 1(a) are extended from the above Type 2 circuits, which have not been studied so far. For the convenience of our work, the representative parameters are selected as R = 10 kΩ and C = 33 nF for the linear circuit elements as well as I S = 5.84 nA, V T = 26 mV and n = 1.94 for the nonlinear 1N4148 diodes.…”

“…Based on a single p -n-junction diode, Sprott (2011) implemented a jerk equation in a jerk circuit form, Srisuchinwong and Treetanakorn (2014) investigated a current-tunable chaotic jerk circuit and Kom et al (2018) studied the asymmetric bistability in a simple autonomous jerk circuit. By combining two operation amplifiers with two diodes and seven resistors, Bao et al (2019) designed a simple realization circuit for absolute value nonlinearity to physically implement a non-autonomous second-order hidden chaotic system.…”

“…In this work, we consider two types of simple jerk circuits. In these two types of simple jerk circuits, one type is achieved by unifying the autonomous jerk circuits dividually reported by Kengne et al (2016), Kom et al (2018) and Sprott (2011), and the other type is extended from the above type of the autonomous jerk circuits. Through switching the states of two switches, three kinds of simple jerk circuits can be obtained from each type of simple jerk circuits.…”

Riddled Attraction Basin and Multistability in Three-Element-Based Memristive Circuit

“…Besides, nonlinear electronic circuits have been counted as powerful candidates in supplying experimental and analytical surveys for people to understand chaotic behaviors in these engineering applications. Nonlinear elements including Chua's diode, PNjunction diode, and memristor, just to refer a few, play a vital role for generating chaos in nonlinear electronic circuits and neuron system [2][3][4][5][6][7][8]. To possess the emblematic characteristics of both nonlinearity and nonvolatile memory [2,3], memristor described by the relation between magnetic flux and electric charge has demonstrated prominent potential in memristor-based applications [4][5][6][7][8][9][10].…”

“…Nonlinear elements including Chua's diode, PNjunction diode, and memristor, just to refer a few, play a vital role for generating chaos in nonlinear electronic circuits and neuron system [2][3][4][5][6][7][8]. To possess the emblematic characteristics of both nonlinearity and nonvolatile memory [2,3], memristor described by the relation between magnetic flux and electric charge has demonstrated prominent potential in memristor-based applications [4][5][6][7][8][9][10]. Particularly, memristor is universally regarded as a basic circuit element that it owns more excellent nonlinearity in constructing chaotic/ hyperchaotic electronic circuits [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and systems [28][29][30][31][32] than classical nonlinearities.…”