Synchronization of the chaotic systems has attracted much attention in recent years due to its vital applications in secured communication systems. In this paper, an implementation and comparative analysis of two different control approaches for synchronization between two identical four-dimensional hyperchaotic systems is presented. The two control approaches are the Adaptive nonlinear controller and the linear optimal quadratic regulator LQR. To demonstrate the effectiveness of each controller, the numerical simulation is presented using Matlab/Simulink and the control law is derived. The performance of the proposed controllers is compared based on four factors; response time, squared error integration, energy applied from the controller, and cost function. To measure the robustness of the control approaches, the performance factors are compared when there is a change in system parameters and a variation in the initial conditions. Then the proposed synchronization methods are implemented on the FPGA platform to demonstrate the utilized resources on Field Programmable Gate Array (FPGA) hardware platform and the operation speed. Finally, to generalize the results of the comparison, the study is implemented for the synchronization of another secured communication system consisting of two identical three-dimensional chaotic. The experimental results show that the LQR method is more effective than the Adaptive controller based on the performance factors we propose. Moreover, the LQR is much simpler to implement on hardware and requires fewer resources on the FPGA.
In this paper, we introduce a category of Novel Jerk Chaotic (NJC) oscillators featuring symmetrical attractors. The proposed jerk chaotic system has three equilibrium points. We show that these equilibrium points are saddle-foci points and unstable. We have used traditional methods such as bifurcation diagrams, phase portraits, and Lyapunov exponents to analyze the dynamic properties of the proposed novel jerk chaotic system. Moreover, simulation results using Multisim, based on an appropriate electronic implementation, align with the theoretical investigations. Additionally, the NJC system is solved numerically using the Dormand Prince algorithm. Subsequently, the Jerk Chaotic System is modeled using a multilayer Feed-Forward Neural Network (FFNN), leveraging its nonlinear mapping capability. This involved utilizing 20,000 values of x1, x2, and x3 for training (70%), validation (15%), and testing (15%) processes, with the target values being their iterative values. Various network structures were experimented with, and the most suitable structure was identified. Lastly, a chaos-based image encryption algorithm is introduced, incorporating scrambling technique derived from a dynamic DNA coding and an improved Hilbert curve. Experimental simulations confirm the algorithm's efficacy in enduring numerous attacks, guaranteeing strong resiliency and robustness.