Homotopy Analysis Method for a Prey-Predator System with Holling IV Functional Response

Abstract

In this paper, the homotopy analysis method is used for solving a prey-predator system with holling IV functional response. The approximation solutions were obtained by homotopy analysis method, and contain the auxiliary parameter h which provides us with a convenient way to adjust and control convergence region and rate of solution series. This result showed that this method is valid and feasible for the system.

Gudermannian neural network procedure for the nonlinear prey-predator dynamical system

“…Recently, numerous schemes have been established to perform the solutions of the NDPPS, e.g., differential transformation approach, Runge–Kutta method, Adomian decomposition technique, Homotopy approach, finite element, Sumudu decomposition scheme, Adams implicit method, reduced fractional differential transformation approach and confidence domain technique [ [15] , [16] , [17] , [18] , [19] , [20] , [21] ]. All these approaches have their own applicability and limitations.…”

Mathematical Analysis of the Prey‐Predator System with Immigrant Prey Using the Soft Computing Technique

“…In recent years, researchers have been working to develop new techniques for finding approximate solutions to nonlinear models; e.g., the Laplace Adomian decomposition method [25], the new coupled fractional reduced differential transform method [26], the Runge-Kutta-Fehlberg method [27], the finite element method [28], the Sumudu decomposition method [29], the implicit Adams methods [30], the confidence domain technique [31], and the homotopy analysis method [32] have become much more significant to get accurate solutions. All these deterministic approaches have their own advantages, applicability, and drawbacks.…”

Soluciones numéricas para diferentes casos del modelo biológico no lineal de presa- depredador

“…Algunos métodos bien conocidos que se han utilizado para resolver el modelo de presadepredador son el método de Runge -Kutta -Fehlberg, transformación diferencial (Batiha, 2014), método de descomposición de Laplace Adomian (Paul, Mondal and Bhattacharya, 2016. ), técnicas de elementos finitos (Garvie et al, 2015), método de análisis de homotopía (Yu and Yu, 2014), método de descomposición Sumudu (Bildik and Deniz, 2016), método de transformación diferencial fraccional (Ray, 2015), y método de dominio de confianza (Bashkirtseva and Ryashko, 2014) .…”