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An Approach for the Generation of an Nth-Order Chaotic System with Hyperbolic Sine
Jizhao Liu1, Jun Ma2, Jing Lian1
1School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China.
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.
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