| Summary: | Nonlinear dynamical systems are ubiquitous in both science and engineering, since the systems allow developing and understanding models of complex systems and phenomena. In this thesis, the complex behaviour of application in secure communication system and mobile robot navigation has been investigated. In chaos-based secure communication schemes, a message signal is modulated to the chaotic signal at transmitter and at receiver the masking signal is regenerated and subtracted from the receiver signal. In order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behaviour as a function of a variable control parameter, has been studied. First, the basic dynamical properties of the Jerk system are analyzed by means of equilibrium points, eigenvalue structures, various attractors, bifurcation diagram, Lyapunov exponent spectrum and Poincare map. Next, the effectiveness of the one way method between two identical Jerk circuits in a secure communication system is presented in details. The numerical simulation by using MATLAB 2010, the implementation of circuit simulations by using MultiSIM 10.0 and the experimental results in laboratory has been performed in this study. Thus, the Jerk system has very good security performance. The last part of this thesis focuses on the analysis of mobile robot navigation. 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 Jerk circuit so that the movement of the robot is very difficult predict. The result of Jerk system shows significantly higher value, where the 75% of the terrain shows to be covered by the robot.
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