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Abstract The primary aim of this thesis is to establish and analyse diverse new chaotic systems and examine their dynamic properties. This category of dynamical systems has numerous applications in engineering, spanning from image processing to economic uses. Chaotic systems are recognized for their sensitivity to initial conditions, where even minor changes in these conditions can result in significant alterations in their outputs. Within this thesis, three novel chaotic systems have been developed and their dynamical characteristics have been examined utilizing the different tools applied in literature such as the eigenvalues method, bifurcation diagrams, Kaplan-Yorke dimension, Lyapunov exponents, time response, phase plane trajectories, and basins of attraction. Furthermore, chaos control in the introduced dynamical systems was investigated through adaptive control and sliding mode control strategies. The objective was to suppress chaotic motion by generating control signals, compelling the system to stabilize at predetermined positions. Also, Chaos synchronization for the proposed chaotic systems was accomplished using adaptive control and sliding mode control methods. A comparative analysis was conducted among different control and synchronization techniques to pinpoint optimized methods for achieving superior control and synchronization efficiency. Additionally, simulations were executed using analogous electronic circuits for the proposed chaotic systems within this thesis to validate the feasibility of implementing such systems. These systems harbour potential applications in various engineering domains, including encryption, secure communications, Biological neural networks, medical systems, and robotics. Finally, the chaotic system is employed as a Pseudo Random Number Generator (PRNG) for image encryption applications using a new encryption model, and experimental results confirm the high security and robustness of the proposed encryption algorithm against various attack methods. |