A 3-D Novel Jerk Chaotic System and Its Application in Secure Communication System and Mobile Robot Navigation

In this work, we study the complex dynamics of a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities, which was proposed by Vaidyanathan et al. Arch Control Sci 24(3):375–403, 2014, [98]. The initial study in this chapter is to analyze the eigenvalue structures, various attractors, Lyapunov exponent analysis, Kaplan Yorke dimension, FFT analysis and Poincare map analysis. We have studied the dynamic behavior of the system in the case of the bidirectional coupling via a linear resistor. Both experimental and simulation results have shown that chaotic synchronization is possible. Furthermore, the effectiveness of the bidirectional coupling method scheme between two identical 3-D novel jerk chaotic systems in a secure communication system is presented in detail. Also, the driving strategy of a mobile robot is studied, in order to generate the most unpredictable trajectory. Kinematics model of the robot’s movement has been created and combined with the networking system of a 3-D novel jerk circuit so that the movement of the robot is very difficult to predict. Finally, numerical simulations by using MATLAB 2010, experimental results, as well as the implementation of circuit simulations by using Proteus has been performed in this study.

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