In this work, we describe the model of a new 5-D hyperchaotic system with three positive Lyapunov exponents. Since the maximum positive Lyapunov exponent of the proposed hyperchaotic system is larger than twelve, the new hyperchaotic system is highly hyperchaotic. We also show that the new 5-D hyperchaotic system exhibits multistability with coexisting attractors. Using Multisim, we design an electronic circuit for the new 5-D hyperchaotic system. The hardware implementation of the new 5-D hyperchaotic system is done by applying two numerical methods. From the experimental results of the FPGA-based implementation, we show that the attractors observed in a Lecroy oscilloscope are in good agreement with numerical simulations. To prove the reliability of the proposed system for cybersecurity purposes, we present a new image cryptosystem using our hyperchaotic system. Experimental outcomes show the efficiency and the reliability of our cryptosystem based on the proposed hyperchaotic system.

In this work, we describe the model of a new 4-D hyperchaotic system with no balance point and deduce that the new hyperchaotic system has a hidden attractor. We present a detailed bifurcation analysis for the new hyperchaotic dynamo system with respect to the system parameters and also exhibit that the new hyperchaotic system displays multistability with coexisting attractors. Using NI Multisim 14.0, we design an electronic circuit for the implementation of the new 4-D hyperchaotic system and present the circuit simulation results. We also show the implementation of the new 4-D hyperchaotic system by using a field programmable gate array (FPGA). The hardware resources are reduced by designing single-constant multipliers, adders, subtractors and multipliers. The FPGA design is done for three numerical methods, namely: Forward-Euler, Backward-Euler and fourth-order Runge-Kutta. We demonstrate that experimental chaotic attractors are in good agreement with theoretical simulations. To verify the ability of the presented hyperchaotic system for designing robust cryptosystems, we suggest a novel image cryptosystem using the proposed hyperchaotic system. Simulation outcomes confirm the effectiveness of the proposed image cryptosystem, and consequently, the effectiveness of the proposed 4-D hyperchaotic system in designing diverse cryptographic purposes.

The very high demand for chaotic systems in the fields of sciences, particularly in secure communication, leads numerous researchers to build novel systems. This work announces a new easy to implement 3D chaotic system with five quadratic nonlinearities and three positive parameters, the proposed system is complex with larger bandwidth compared to at least 50 other systems that have been described. It contains eight terms and it can generate chaotic, periodic and quasi-periodic behaviors. The main dynamical properties of the proposed system are studied using Kaplan-Yorke dimension (KYD), Lyapunov exponents, bifurcation diagrams, multistability, equilibrium points stability and dissipativity. Then, the eight terms system feasibility is verified using Multisim software by designing its electronic circuit. In addition, active controllers are designed for leading the proposed system to achieve stability, tracking a desired dynamic and synchronizing with an identical model. Finally, using drive response synchronization, a novel secure communication electrical circuit design is built based on the suggested approach. The findings from numerical experiment demonstrated the new system’s success in completing the encryption/decryption process, as well as its secured transmission technique.

Chaotic systems are known to be extremely sensitive to initial conditions, meaning small changes can have a significant impact on the outcomes. By analyzing the average profit margin in relation to chaotic dynamics, companies can conduct sensitivity analysis to assess the potential impact of various factors on their profitability. This analysis can help identify critical variables or scenarios that may significantly affect profit margins. In this article, we have proposed a hyperchaotic financial system with sinusoidal hyperbolic non-linear variables applied to the average profit margin. Furthermore, we have investigated the stability of the hyperchaotic financial dynamics model to provide information to companies to assess the consistency and reliability of their profitability. In addition, fundamental dynamic behavior like Lyapunov exponents, bifurcation analysis, coexisting attractors have been reported. Finally, a nonlinear feedback control approach is developed to train an adaptive neural fuzzy controller. The application of Lyapunov theory confirms that this nonlinear feedback controller can effectively minimize the synchronization error within a finite duration. The results from simulations establish the effectiveness of the proposed neural fuzzy controller architecture in controlling the synchronization of two hyperchaotic financial models. Additionally, the simulation includes a comparison between the performance of the nonlinear controller and the adaptive neural fuzzy controller.

Mechanical jerk systems have applications in several areas, such as oscillators, microcontrollers, circuits, memristors, encryption, etc. This research manuscript reports a new 3-D chaotic jerk system with two unstable balance points. It is shown that the proposed mechanical jerk system exhibits multistability with coexisting chaotic attractors for the same set of system constants but for different initial states. A bifurcation analysis of the proposed mechanical jerk system is presented to highlight the special properties of the system with respect to the variation of system constants. A field-programmable gate array (FPGA) implementation of the proposed mechanical jerk system is given by synthesizing the discrete equations that are obtained by applying one-step numerical methods. The hardware resources are reduced by performing pipeline operations, and, finally, the paper concludes that the experimental results of the proposed mechanical jerk system using FPGA-based design show good agreement with the MATLAB simulations of the same system.