In this paper, we propose and analyze a fractional prey–predator model with generalized Hattaf fractional (GHF) derivative. We prove that our proposed model is ecologically and mathematically well-posed. Furthermore, we show that our model has three equilibrium points. Finally, we establish the stability of these equilibria.
This paper presents theoretical and numerical study of a stochastic SIRC epidemic model with time delay and nonlinear incidence. The existence and uniqueness of a global positive solution is proved. The Lyapunov analysis method is used to obtain sufficient conditions for the existence of a stationary distribution and the disease extinction under certain assumptions. Numerical simulations are also elaborated for the considered stochastic model in order to corroborate the theoretical findings.
Motivated by some biological and ecological problems given by reaction-diffusion systems with delays and boundary conditions of Neumann type and knowing their associated Lyapunov functions for delay ordinary differential equations, we consider a method for determining their Lyapunov functions to establish the local/global stability. The method is essentially based on adding integral terms to the corresponding Lyapunov function for ordinary differential equations. The new approach is not general but it is applicable in a wide variety of delays reaction-diffusion models
In this article there has been conducted analysis of Lyapunov matrix application in order to form control inputs under different dynamic systems’ optimization methods oriented by quadratic integral criterion. For this purpose, the methods of finding the Lyapunov matrix and optimization based on the Bellman functional equation with subsequent application of the Riccati equation, optimization taking into account the initial values of state variables, optimization based on the Bellman equation using linear matrix inequalities and Lyapunov equation are considered.