On the analytical study of predator–prey model with Holling-II by using the new modified extended direct algebraic technique and its stability analysis

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.