Rajendran Samidurai

Finite-time Lyapunov exponents (FTLEs) quantify short-horizon trajectory divergence and provide a local, spatially resolved view of transient instabilities and synchronization behavior in nonlinear dynamics. This work studies a class of fractional-order complex-valued bidirectional associative memory (BAM) neural networks and proposes a unified analytical and data-driven framework for synchronization and local stability assessment. Using fractional Lyapunov stability theory together with Mittag-Leffler functions, sufficient conditions are derived to guarantee global Mittag-Leffler synchronization of the drive-response systems under a linear error-feedback controller. In addition, an explicit conservative time-to-tolerance estimate is obtained via a standard upper bound on the Mittag-Leffler function. Numerical simulations corroborate the theory and demonstrate rapid decay of synchronization errors in both real and imaginary state components. To complement the model-based guarantees, two trajectory-driven Lyapunov proxies are introduced: (i) micro-ensemble FTLE estimation based on the geometric-mean growth of small perturbations, and (ii) a k-nearest neighbors (kNN) prediction-error index that quantifies local instability through short-term forecast errors. Both proxies reveal oscillatory transient divergence patterns and consistently reflect the stabilizing effect of the designed controller. The proposed integration of fractional calculus, synchronization control, and data-driven Lyapunov diagnostics provides a robust methodology for complex-valued fractional-order neural networks, with potential applications in secure communications and nonlinear signal processing.

The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov–Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings.

Stochastic disturbances often cause undesirable characteristics in real-world system modeling. As a result, investigations on stochastic disturbances in neural network (NN) modeling are important. In this study, stochastic disturbances are considered for the formulation of a new class of NN models; i.e., the discrete-time stochastic quaternion-valued neural networks (DSQVNNs). In addition, the mean-square asymptotic stability issue in DSQVNNs is studied. Firstly, we decompose the original DSQVNN model into four real-valued models using the real-imaginary separation method, in order to avoid difficulties caused by non-commutative quaternion multiplication. Secondly, some new sufficient conditions for the mean-square asymptotic stability criterion with respect to the considered DSQVNN model are obtained via the linear matrix inequality (LMI) approach, based on the Lyapunov functional and stochastic analysis. Finally, examples are presented to ascertain the usefulness of the obtained theoretical results.