In this paper, we propose a new five-dimensional system that is capable of producing multistability and hyperchaos with three positive Lyapunov exponents (LEs) for specific parameter settings. The proposed system was derived by making an extension of Dong's chaotic system with changes that increase its dimension, complexity, and applicability. Using numerical simulations, we confirmed that the model produces hyperchaos with three positive LEs depending on parameter values, which means that its dynamics expands in three directions of the phase space. Regions of periodicity, chaos, hyperchaos with two positive LEs, and hyperchaos with three positive LEs were identified by LE spectra and verified using phase diagrams. The ability of the system to generate coexisting attractors is also shown, where the system demonstrates various behaviors for various initial conditions at fixed parameters. Furthermore, offset boosting control is presented to show that the attractors can be shifted without altering the internal dynamics of the system. Moreover, a topological complexity optimization framework is proposed to maximize the Kaplan–Yorke dimension (KYD) using Particle Swarm Optimization (PSO) and Differential Evolution (DE), followed by the 0–1 test and Approximate Entropy calculation. With its multistability, properties, hyperchaos with three positive LEs, controllable offset boosting, and optimized complexity, the novel model has excellent potential for practical applications.

In this paper, we investigated the chaotic behavior of a Jerk system proposed by Sambas et al. (2024), which features symmetrical attractors arising from the interplay of sinusoidal, hyperbolic, and absolute nonlinearities. The system's complex dynamics were analyzed using established numerical methods such as phase portraits, stability analysis, bifurcation diagrams, and Lyapunov exponents. Furthermore, through amplitude modulation, we showed that the control parameter δ can enhance or attenuate signal amplitudes without disrupting the system's stability or chaotic nature. The theoretical findings were further validated through Multisim circuit simulations, with experimental attractors closely matching the numerical results. In addition, a Radial Basis Function Neural Network (RBFNN) was implemented to approximate the chaotic trajectories of the system. The model was trained using simulated data and optimized via the least squares method. Network performance was evaluated using Root Mean Square Error (RMSE) and relative error. The results showed that the RBFNN accurately predicts the system's state variables, achieving MSE values on the order of 10^-10–10^-9 and relative error below 1.1 × 10^-8.