**Abstract**

In recent years, exploring and investigating chaotic systems with hyperbolic sine nonlinearity has gained the interest of many researchers. With two back-to-back diodes to approximate the hyperbolic sine nonlinearity, these chaotic systems can achieve simplicity of the electrical circuit without any multiplier or sub-circuits. In this chapter, the genesis of chaotic systems with hyperbolic sine nonlinearity is introduced, followed by the general method of generating nth-order (n > 3) chaotic systems. Then some derived chaotic systems/torus-chaotic system with hyperbolic sine nonlinearity is discussed. Finally, the applications such as random number generator algorithm, spread spectrum communication and image encryption schemes are introduced. The contribution of this chapter is that it systematically summarizes the design methods, the dynamic behavior and typical engineering applications of chaotic systems with hyperbolic sine nonlinearity, which may widen the current knowledge of chaos theory and engineering applications based on chaotic systems.

**Keywords:** chaotic systems, torus chaos, hyperbolic sine nonlinearity, spread spectrum communication, image encryption
