M. Lellis Thivagar

Parameter identification techniques for linear and nonlinear dynamic systems currently show a clear orientation toward black box models, with Artificial Neural Networks occupying a prominent place there. This paper presents a procedure for identifying linear dynamic systems parameters in two stages: in the first, a regressive model is fitted from the excitation and response time records, and in the second, its parameters are identified (matrixes of stiffness and damping) and dynamic characteristics (vibration frequencies and modes) based on the previous model. Artificial Neural Networks of the Adaline type and multilayer Perceptions are used for the first stage. The second stage is fully formulated through matrix algebra, which facilitates its systematic implementation and makes it independent of the complexity or dimension of the studied system. The proposed procedure is intended to operate from experimental records, so special attention is paid to the sensitivity of the results to the data interval and noise in the input signals. For the latter, various noise levels were incorporated into the correct responses obtained under ideal conditions, which respond to Gaussian distribution functions with a null mean and specified standard deviation. The proposed procedure justification, the results with the regressive models, and a study of the sensitivity of the results to the variation in the available data quality are presented.

In the many approaches to soft set theory, the theory of N-soft topological space is a key component of studying topology. The notions of soft mapping in N-soft topological space as well as a novel notion of N-soft continuous mapping, N-soft quotient mapping, and N-soft quotient topology are discussed in this article. We also look at some of its traits and outcomes. It will give the foundation for real-world applications in this subject.

This study focuses on hybrid synchronization, a new synchronization phenomenon in which one element of the system is synced with another part of the system that is not allowing full synchronization and nonsynchronization to coexist in the system. When , where Y and X are the state vectors of the drive and response systems, respectively, and Wan ( = 1)), the two systems’ hybrid synchronization phenomena are realized mathematically. Nonlinear control is used to create four alternative error stabilization controllers that are based on two basic tools: Lyapunov stability theory and the linearization approach.

In this study, a novel 7D hyperchaotic model is constructed from the 6D Lorenz model via the nonlinear feedback control technique. The proposed model has an only unstable origin point. Thus, it is categorized as a model with self‐excited attractors. And it has seven equations which include 19 terms, four of which are quadratic nonlinearities. Various important features of the novel model are analyzed, including equilibria points, stability, and Lyapunov exponents. The numerical simulation shows that the new class exhibits dynamical behaviors such as chaotic and hyperchaotic. This paper also presents the hybrid synchronization for a novel model via Lyapunov stability theory.

Chaotic systems are one of the most significant systems of the technological period because their qualities must be updated on a regular basis in order for the speed of security and information transfer to rise, as well as the system’s stability. The purpose of this research is to look at the special features of the nine‐dimensional, difficult, and highly nonlinear hyperchaotic model, with a particular focus on synchronization. Furthermore, several criteria for such models have been examined; Hamiltonian, synchronizing, Lyapunov expansions, and stability are some of the terms used. The geometrical requirements, which play an important part in the analysis of dynamic systems, are also included in this research due to their importance. The synchronization and control of complicated networks’ most nonlinear control is important to use and is based on two major techniques. The linearization approach and the Lyapunov stability theory are the foundation for attaining system synchronization in these two ways.