A New 5-D Hyperchaotic System With a Line Equilibrium, Its Bifurcation Analysis, Circuit Simulation, FPGA Implementation, and Data Prediction Using Long-Term-Short Memory

This work proposes a new 5-D hyperchaotic system with a line of equilibrium points. The bifurcation properties of the new hyperchaotic system are analyzed using bifurcation diagrams and Lyapunov exponents spectra. Multistability and offset boosting properties of the new hyperchaotic system are also discussed. With the help of Multisim 14.0 circuit simulator, an electronic circuit design for the new 5-D hyperchaotic system with a line of equilibrium points has been constructed. Furthermore, an FPGA implementation of the proposed hyperchaotic system is performed by applying Forward Euler numerical methods using FPGA CYCLONE IV GX platform. Additionally, this study demonstrates the use of the Long-Short-Term Memory LSTM model to predict the future hyperchaotic behavior of the new 5-D hyperchaotic system. The Mean Square Error (MSE), Root Mean Square Error (RMSE), and the coefficient of determination ( $R^{2}$ ) metrics are used to evaluate the prediction performance of the proposed LSTM model. The small obtained values for MSE and RMSE respectively, along with $R^{2}$ scores near to 1, reveal the accuracy and reliability of the proposed prediction model.