5 papers · 1 filter
A simple second-order nonstandard numerical method for a general class of dynamical systems and its applications
Manh Tuan Hoang
In this work, we consider a class of continuous-time autonomous dynamical systems that model various important phenomena and processes encountered in real-world situations. We cons…
A Generalized Hacker Dynamics Model with Nonlinear Incidence: Analysis and Positivity-Preserving Numerical Simulation
Manh Tuan Hoang, Hoai Thu Pham, Matthias Ehrhardt
We propose and analyze a generalized compartment model for hacker dynamics in cybersecurity systems. This model is an extension of a recently introduced framework, replacing the bi…
A Generalized Second-Order Positivity-Preserving Numerical Method for Non-Autonomous Dynamical Systems with Applications
Manh Tuan Hoang, Matthias Ehrhardt
In this work, we propose a generalized, second-order, nonstandard finite difference (NSFD) method for non-autonomous dynamical systems. The proposed method combines the NSFD framew…
Nonstandard finite difference methods preserving general quadratic Lyapunov functions
Manh Tuan Hoang
In this work, we consider a class of dynamical systems described by ordinary differential equations under the assumption that the global asymptotic stability (GAS) of equilibrium p…
A generalized nonstandard finite difference method for a class of autonomous dynamical systems and its applications
Manh Tuan Hoang
In this work, a class of continuous-time autonomous dynamical systems describing many important phenomena and processes arising in real-world applications is considered. We apply t…