An Analysis on One Prey and Two Predator Model in Variable Order Using Neural Network Approach

ABSTRACT

This research examines a mathematical model for one prey and two predators with disease in the predator. The entire population is divided into three classes: prey, sound predators, and infected predators. Regarding the sound predator and the diseased predator, respectively, two different nonlinear prey refuge coefficients have been investigated. The complexity and dynamic nature of this model are analyzed using the derivatives framework, the fractal‐fractional (F‐F) in Caputo sense, and the Caputo‐Fabrizio (CF) sense. Fixed‐point theory has been used to determine the existence and uniqueness of a solution. To solve the model, we employ numerical techniques and the Levenberg‐Marquardt Neural Network (LMNN). Twelve neurons in the supervised learning framework have a log‐sigmoid transfer function. Testing, training, and validation were completed in the following percentages: 13%, 74%, 13%. Regression plots, histogram curves, correlation analysis, and function fit testing are used to assess the model's predictive accuracy. The sound predator and the infected predator give better information for the proposed model. In order to stop the spread of infection, harvesting criteria are essential. In the numerical simulation section, a suitable graphical representation and discussions are conducted to support the proposed model. The nonlinear competitive parameters , , , and have been examined in connection with Hopf bifurcation analysis. All things considered, the study's findings are novel and significant, making them a valuable and intriguing contribution to the field of theoretical prey‐predator.