Stabilizing Unstable Periodic Orbits of the Multi-Scroll Chua’s Attractor

Controlling chaos has become a challenging topic in nonlinear dynamics. It has been studied in many scientific and engineering fields such as physics, chemistry, electrical circuit, etc., and several extension and applications of the original OGY control method [1] have been reported [2–6]. Chua’s circuit is known as an electrical circuit and having the ability of generating chaos [7]. Recent research results include modifying its nonlinear characteristics by using a generalized piecewise linear function (PWL) with multiple breakpoints to generate the so-called multi-scroll chaotic attractor. Suykens and Vandewalle [8] designed a simple recurrent neural network model that can produce a chaotic attractor like the double-scroll attractor of Chua’s circuit. Later on, Suykens et al. [9] proposed a method for generating a more complete family of multiscroll instead of n-double scroll chaotic attractors. In [10], the author presented a PWL function approach for creating multi-spiral chaotic attractors from both autonomous and non autonomous differential equations. Yalcin et al. [11,12] also proposed a simple circuit model for generating n-scroll chaotic attractors. The main design idea of most of the aforementioned methodologies is the same – to add some additional breakpoints into the PWL function of the nonlinear resistor in Chua’s circuit, or other nonlinear circuits [13]. Most, if not all, of the aforementioned multi-scroll chaotic attractors were verified only by numerical simulations. However, known to electronic engineers, it is much more difficult to physically realize these multi-scroll chaotic attractors by analogue circuits. But