On the analytical study of predator–prey model with Holling-II by using the new modified extended direct algebraic technique and its stability analysis
Tahir Shahzad, Muhammad Zafarullah Baber, Muhammad Ahmad, Nauman Ahmed, Ali Akgül, Syed Mansoor Ali, Mubasher Ali, Sayed M. El Din
Abstract
The current study is concerned with a predator–prey model with a functional response of Holling type II that includes prey refuge and diffusion. These types of equations arise in different fields, such as biomathematics ,biophysics, polymer rheology, agriculture, thermodynamics, blood flow phenomena, aerodynamics, capacitor theory, electrical circuits, electron-analytical, chemistry, control theory, fitting of experimental data. The underlying model is analytically investigated by a technique, namely a new extended direct algebraic method (NEDAM). The single and combined wave solutions are observed in shock, complex solitary-shock, shock-singular, and periodic-singular forms. The rational solutions are also emerged during the derivation. The stability of the model is discussed. There is also a section about unique physical problems. The 3D, 2D, and line graphs are plotted for different values of parameters.