A modified neural network method for computing the Lyapunov exponent spectrum in the nonlinear analysis of dynamical systems

• The study presents an innovative approach using a neural network to compute the Lyapunov exponent spectrum, a key measure for assessing the dynamics of chaotic systems. • Comparisons are made with established algorithms such as Benettin, Wolf, Rosenstein, Kantz, Synchronisation and the Sano-Sawada algorithm. • The methods are applied to solve classical nonlinear dynamics problems such as the generalised Hénon map, the chaotic attractor of the Baier-Klein map, and mechanical vibrations in structures such as the flexible Bernoulli-Euler beam and functionally graded porous cylindrical shells under alternating loads. • The modified neural network method shows superior performance in terms of sample size and accuracy compared to traditional methods and, importantly, does not require knowledge of the initial system equations. This study presents a modified neural network method for computing the Lyapunov exponent spectrum in non-linear dynamical systems. Its mathematical description is an introduction. The proposed modified neural network method allows the addition of bias and constant neurons to the neural network topology and the use of different numbers of activation functions to suit different cases. Various algorithms for computing Lyapunov exponents, such as the Benettin method, the Wolf method, the Rosenstein method, the Kantz method, the Synchronisation method, the Sano-Sawada algorithm and the proposed modification of the neural network method, are used for classical problems in nonlinear dynamics . These problems include the generalised Hénon map, the chaotic attractor of the Baier-Klein map, and the vibrations of mechanical systems such as the flexible Bernoulli-Euler beam and the flexible functionally graded porous closed cylindrical shell under alternating load. The comparative analyses presented in this study are aimed at validating the accuracy and effectiveness of the methods, and at identifying the most relevant approaches for different types of systems and classes of problems. The proposed method is demonstrated to be superior to existing methods based on time-series evaluation in terms of sample size and accuracy. Furthermore, it does not require the initial system equations.