A Chaotic Time-Delay System with Saturation Nonlinearity

1. Introduction

Chaos theory has received significant attentions in last decades (Lorenz, 1963; Anishchenko, 1993; Grebogi, 1997; Hasselblatt, 2003; Davies, 2004; Banerjee, 2011; Azar & Vaidyanathan 2015a, b, c; Zhu & Azar, 2015; Azar & Zhu, 2015). Various chaotic systems and their synchronization schemes have presented in the literature (Vaidyanathan & Azar, 2015a, b, c, d; Vaidyanathan et al., 2015a, b, c; Pham, 2015). In fact, chaos appears naturally in weather and climate, biology, sociology, and physics etc. (Strogatz, 1994; Holland, 1998; Hilborn, 2000). Moreover, chaotic systems with their complex characteristics have also been successfully utilized in diverse applications, ranging from secure chaotic communications (Cuomo, 1993), chaotic cryptography (Kocarev, 2001; Alvarez, 2006; Koc, 2009; Kocarev, 2011), information encryption (Zhang, 2005; Tong, 2009; Wang, 2012; Seyedzadeh, 2012; Volos, 2013), economics (Medio, 2009), robotics (Volos, 2012), to liquid shakers (Zhang, 2007) and so on.