Generating 3-Scroll Attractors From One Chua Circuit

Abstract

This paper reports the finding of a 3-scroll chaotic attractor with only three equilibria obtained via direct modification of Chua's circuit. In addition, it is shown numerically that the new system can also generate one-scroll and two-scroll chaotic attractors.

Design and Applications of Continuous-Time Chaos Generators

“…A significant feature of these functions is that they are smooth enough to possess convergent Taylor expansions at all points and consequently can be linearized (Strogatz, 2001). A type of nonlinear function frequently used in system modeling is the piecewise-linear (PWL) approximation, which consists of a set of linear relations valid in different regions (Elhadj & Sprott, 2010;Lin & Wang, 2010;Lü et al, 2004;Muñoz-Pacheco & Tlelo-Cuautle, 2009;Sánchez-López et al, 2010;Suykens et al, 1997;Yalçin et al, 2002). The use of PWL approximations have the advantage that the dynamical equations become linear or linearized in any particular region, and hence the solutions for different regions can be joined together at the boundaries.…”

“…In electronics, among the currently available chaotic oscillators, Chua's circuit has been the most used one (Chakraborty & Dana, 2010;Elhadj & Sprott, 2010;Sánchez-López et al, 2008;Senani & Gupta, 1998;Suykens et al, 1997;Trejo-Guerra et al, 2009), because it can be easily built, simulated, and tractable mathematically. It consists of five circuit elements: one linear resistor, one inductor, two capacitors, and one nonlinear resistor known as Chua's diode (Tlelo-Cuautle et al, 2006).…”

“…The design of multi-scroll chaotic attractors can be performed via PWL functions (Elhadj & Sprott, 2010;Lin & Wang, 2010;Lü et al, 2004;Muñoz-Pacheco & Tlelo-Cuautle, 2009; Yalçin et al, 2002). In the case of Chua's circuit based oscillators, the PWL function is designed by introducing additional breakpoints to Chua's diode (Trejo-Guerra, Sánchez-López, Tlelo-Cuautle, Cruz-Hernández & Muñoz-Pacheco, 2010), or by generalizing Chua's circuit as proposed in (Suykens et al, 1997;Yalcin et al, 2000).…”

Novel 3-Scroll Chua’s Attractor with One Saddle-Focus and Two Stable Node-Foci

“…Different Chua's nonlinearities formulate the three equilibrium points with different characteristics, leading to the generations of different types of Chua's attractors. This paper finds 2-scroll and 3-scroll Chua's attractors in the classic Chua's system by setting the outer segment slope of threesegment piecewise-linearity to be positive and introducing a new piecewise-linear control function [10,28]. A distinct characteristic is that the scroll number of the new Chua's attractor does not associate with the number of index-2 saddle-foci of the classic Chua's system.…”

“…By modifying Chua's nonlinearity with multiple-segment piecewise-linear or continuous nonlinear functions, Chua's system can be generalized to a system exhibiting more complex attractors [8][9][10], that is, self-excited multiscroll Chua's chaotic attractors. Generally, self-excited multiscroll or multiwing chaotic attractors are generated by disposing unstable index-2 saddle-foci in terms of added breakpoints in the model system [11,12], which shows great theoretical and practical significance due to the applications to encrypted communication, chaos synchronization, and some other fields of Chua's systems with multiscroll chaotic attractors [13].…”