Dynamical Analysis of a Novel 4-D Hyper-Chaotic System With One Non-Hyperbolic Equilibrium Point and Application in Secure Communication

1. Introduction

The study of chaotic systems to unveil their complex and rich dynamics has gained strength ever since the Lorenz system (Luo, 2009) (Mahmoud & Mahmoud, 2010)(Wu, Zhang & Zhong, 2019) was discovered in 1960. The scientific community worldwide got interested in taming chaos (total randomness) either by synchronizing chaotic systems or controlling chaos (Khan & Bhat, 2016)(Singh, Yadav & Das,2016). Synchronization (1990) (Pham, Jafari, Wang & Ma, 2016)(Mahmoud & Mahmoud, 2012) involves the process of locking the dynamics of one system into the other. Many synchronization techniques have been developed such as complete synchronization, anti-synchronization (Jimenez-Triana, Chen & Gauthier, 2015) (Karavaev, Kulminskiy, Ponomarenko & Prokhorov, 2015), hybrid synchronization (Khan, Khattar & Prajapati, 2017) (Khan & Bhat, 2017), projective synchronization, function projective synchronization, modified function projective synchronization, phase synchronization (Jafari, Pham & Kapitaniak, 2016), lag synchronization (Jafari, Sprott & Molaie, 2016)(Guo, 2011), combination synchronization, combination-combination synchronization, compound synchronization etc (Khan, Khattar & Prajapati, 2017)(Khan & Tyagi, 2018)(Khan & Singh, 2017) (Kousaka, Ueta & Kawakami, 1999)(Li, Hu, Sprott & Wang, 2015) using various control techniques such as Active Control, Adaptive Control (Park, 2005)(Torrieri,1985) (Vaidyanathan,2014), Sliding Mode Control, Tracking Control, Optimal Control (Skardal, Sevilla-Escoboza, Vera-Aviia & Buldu, 2017) etc. (Othman, Noorani & Al-sawalha,2017)(Ghabi, Rhif & Vaidyanathan, 2018) (Bouzaida & Sakly, 2018) (Balochian & Rajaee, 2018)