Application of the Generalized Backstepping Control Method for Lotka-Volterra Prey-Predator System with Constant Time Delay

Abstract

A well-known method, namely the backstepping method, which is used for stabilizing systems of ordinary differential equations is applied in this paper to solve the system of Lotka-Volterra prey-predator with time delay. The followed approach is accomplished with the cooperation of the method of steps, which is a well-known approach followed in solving delay differential equations, to transform the system of nonlinear delay differential equations into an equivalent system of ordinary differential equations. The fundamental concept behind the backstepping method is to construct recursively Lyapunov functions in quadratic form to stabilize the system for each time step interval. Matlab computer software is used to carry out the numerical simulation in order to investigate the effectiveness of the followed approach.

Solving Multispecies Lotka–Volterra Equations by the Daftardar-Gejji and Jafari Method

“…Te Lotka-Volterra equations were solved by many numerical methods like hybrid deep network [17], Gröbner bases elimination method [18], generalized backstepping control method [19], the diferential transformation method (DTM) [20], the Adomian decomposition method (ADM), and variational iteration method (VIM) [21].…”