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.
Highlights
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. As it has been shown, Chua’s circuit is a relatively simple circuit which has rapidly become a paradigm for chaos [1]
In the past three decades, numerous works have been reported on this circuit, including realization schemes, experimental measurements, numerical observations, and theoretical proofs [2,3,4,5,6,7]
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]
Summary
As it has been shown, Chua’s circuit is a relatively simple circuit which has rapidly become a paradigm for chaos [1]. The classic Chua’s system has three unstable equilibrium points, one zero index-1 saddle-focus and two symmetric nonzero index-2 saddle-foci, resulting in the generation of a self-excited 2-scroll chaotic attractor [1]. Different from self-excited attractor, hidden attractor, whose attraction basin does not intersect with small neighborhoods of the equilibria of the system [19,20,21], is sensitive to the initial conditions and special analytical-numerical procedure should be adopted to locate its attractive basin [20] By developing this procedure, hidden chaotic spiral attractor has been numerically observed in the classic Chua’s system with one stable zero equilibrium point [20, 26].
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