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Abstract
Oscillations and oscillators appear in various fields and find applications in numerous areas. We present an oscillator with infinite equilibria in this work. The oscillator includes only nonlinear elements (quadratic, absolute, and cubic ones). It is different from common oscillators, in which there are linear elements. Special features of the oscillator are suitable for secure applications. The oscillator’s dynamics have been discovered via simulations and an electronic circuit. Chaotic attractors, bifurcation diagrams, Lyapunov exponents, and the boosting feature are presented while measurements of the implemented oscillator are reported by using an oscilloscope. We introduce a random number generator using such an oscillator, which is applied in biomedical image encryption. Moreover, the security and performance analysis are considered to confirm the correctness of encryption and decryption processes.
Highlights
Nonlinear systems are studied widely because of their complex dynamics [1,2,3,4,5]
Chaos was reported in various systems such as the spherical system [8], the plasma model [9], the jerk circuit [10], the modified logistic map [11], the complex Rikitake model [12], and the glucose-insulin system [13]
In the work [26], the authors applied absolute and quadratic terms to get a gallery of systems, in which equilibria are located on lines and curves
Summary
Nonlinear systems are studied widely because of their complex dynamics [1,2,3,4,5]. In the work [26], the authors applied absolute and quadratic terms to get a gallery of systems, in which equilibria are located on lines and curves. The presence of infinite equilibria has received considerable critical attention [31,32], there are still issues which should be considered further [24]. The purpose of this investigation is to explore an oscillator with infinite equilibria.
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