Abstract
Chaotic systems with hyperbolic sine nonlinearity have attracted the attention of researchers in the last two years. This paper introduces a new approach for generating a class of simple chaotic systems with hyperbolic sine. With nth-order ordinary differential equations (ODEs), any desirable order of chaotic systems with hyperbolic sine nonlinearity can be easily constructed. Fourth-order, fifth-order, and tenth-order chaotic systems are taken as examples to verify the theory. To achieve simplicity of the electrical circuit, two back-to-back diodes represent hyperbolic sine nonlinearity without any multiplier or subcircuits. Thus, these systems can achieve both physical simplicity and analytic complexity at the same time.
Highlights
Chaos is commonly associated with entropy [1]
The others are continuous-time chaotic systems [15]. These systems are in the form of autonomous ordinary differential equations (ODEs) with at least three variables and one nonlinearity [16]. This is because the Poincaré–Bendixson theorem implies that a two-dimensional continuous dynamical system cannot give rise to a chaotic system [17]
Fourth-order, fifth-order, and tenth-order chaotic systems are taken as examples
Summary
Chaos is commonly associated with entropy [1]. For example, positive entropy is one of the most important ways to understand chaos [2]. The others are continuous-time chaotic systems [15] These systems are in the form of autonomous ordinary differential equations (ODEs) with at least three variables and one nonlinearity [16]. Continuous-time chaotic systems have many practical applications, to name just a few, they have been widely used in image encryption [18], secure communication [19], and liquid mixing [20] To achieve simplicity of an electrical circuit, two back-to-back diodes represent hyperbolic sine nonlinearity without any multiplier or subcircuits These systems could satisfy all three kinds of simplicities at the same time.
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