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

Abstract

With new three-segment piecewise-linearity in the classic Chua's system, two new types of 2-scroll and 3-scroll Chua's attractors are found in this paper. By changing the outer segment slope of the three-segment piecewise-linearity as positive, the new 2-scroll Chua's attractor has emerged from one zero index-1 saddle-focus and two symmetric stable nonzero node-foci. In particular, by newly introducing a piecewise-linear control function, an improved Chua's system only with one zero index-2 saddle-focus and two stable nonzero node-foci is constructed, from which a 3-scroll Chua's attractor is converged. Some remarks for Chua's nonlinearities and the generating chaotic attractors are discussed, and the stabilities at the three equilibrium points are then analyzed, upon which the emerging mechanisms of the novel 2-scroll and 3-scroll Chua's attractors are explored in depth. Furthermore, an analog electronic circuit built with operational amplifier and analog multiplier is designed and hardware circuit experiments are measured to verify the numerical simulations. These novel 2-scroll and 3-scroll Chua's attractors reported in this paper are completely different from the classic Chua's attractors, which will enrich the dynamics of the classic Chua's system.

Probing 3D chaotic Thomas’ cyclically attractor with multimedia encryption and electronic circuitry

“…Deterministicnonlinear dynamical systems, widely known as chaos, have now been considered as an interdisciplinary subject with applications in the fields of physics [1,2], biology [3], economics [4], medicine [5], communication [6], cryptography [7], electronics [8,9] etc. The evolution of chaos after Lorenz [10], a two-scroll chaotic attractor led to the development of one scroll attractor [11], three scroll attractor [12], six scroll attractor [13], and multi-scroll attractor [14]. The attractors were studied and researched in detail, such as limit cycle attractors presented by Vanderpole [15] in his study of force triod vibration, a model of electronic circuits that was used in radio.…”