Abstract
This work presents a multiscroll generator system, which addresses the issue by the implementation of 9-level saturated nonlinear function, SNLF, being modified with a new control parameter that acts as a bifurcation parameter. By means of the modification of the newly introduced parameter, it is possible to control the number of scrolls to generate. The proposed system has richer dynamics than the original, not only presenting the generation of a global attractor; it is capable of generating monostable and bistable multiscrolls. The study of the basin of attraction for the natural attractor generation (9-scroll SNLF) shows the restrictions in the initial conditions space where the system is capable of presenting dynamical responses, limiting its possible electronic implementations.
Highlights
Over the last few years, the development and implementation of chaotic oscillators have been extensively studied, taking a special interest in the generation of systems with multiscrolls in their phase space, such as the Lorenz [1] and Chua [2] systems, which present a double-scroll attractor
As an alternative to this dilemma arises, the conception of a saturated nonlinear function, SNLF, which is based on the operational amplifiers performance [11, 12], which guarantees to find as many scrolls as segmentation points the function possesses, being a simpler way to approach the topic in the scrolls generation
This is because the scrolls generation is produced gradually, obtaining a greater number of generated dynamics, unlike the behavior displayed in other values of the control parameter
Summary
Over the last few years, the development and implementation of chaotic oscillators have been extensively studied, taking a special interest in the generation of systems with multiscrolls in their phase space, such as the Lorenz [1] and Chua [2] systems, which present a double-scroll attractor. Any three-dimensional dynamic system is considered an UDS if and only if it has a combination of eigenvalues that coincide with the definition of a hyperbolic saddle-node, and the sum of these components is negative, i.e., the dissipation condition is fulfilled [15] Examples of these systems are found in Rössler [16], Lorenz [1], and Chua [2], among some other systems [17,18,19]. This kind of combination in the eigenvalues favors the appearance of multiscroll behavior, by means of the implementation of the appropriated nonlinear function
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