Autoregressive exogenous neural structures for synthetic datasets of olive disease control model with fractional...

A fundamental element of the Mediterranean diet, olive oil is abundant in heart-healthy monounsaturated fats and antioxidants, lowering the risk of cardiovascular diseases. However, the olive oil industry confronts hurdles arising from olive tree diseases, despite the numerous health advantages associated with its consumption. In pursuit of research goals, this study endeavors to employ cutting-edge intelligent computing paradigms, specifically nonlinear autoregressive exogenous neural networks utilizing the Levenberg-Marquardt scheme (NNLMS), to comprehensively analyze the complex dynamic interactions of the fractional-order olive disease control (FO-ODC) model. In the realm of nonlinear fractional differential modeling, this study explores a system governed by four distinct populations: the branches and leaves of healthy olive trees, olive trees affected by a detrimental fungus, a pathogenic filamentous fungus causing infection and damage to olive leaves, and branches, and the microbial organisms residing in the phyllosphere. The research aims to scrutinize the transmission patterns of olive disease within this complex ecological framework. Employing the fractional Grünwald-Letnikov backward finite difference method, this study undertakes the generation of a synthetic dataset that accurately illustrates variations in several key parameters, including the rate of healthy leaf production, natural mortality rate, growth rate of beneficial fungi, nutrient acquisition rate by pathogens from infected leaves, the scaling factor governing food acquisition in their mutualistic relationship, and the rate at which leaves are adversely affected or degrade due to the influence of harmful fungi. In each iteration of the NNLMS application, the synthetic dataset is arbitrarily segmented into training, testing, and validation samples, facilitating the computation of an approximate solution for the dynamics embedded in the nonlinear FO-ODC model. The viability of the design approach is evaluated/assessed by consistently matching outcomes with reference solutions through numerous variations of the FO-ODC model. The reliability and efficiency of the design approach are measured using various measures, such as regression analysis, absolute errors, mean errors, autocorrelations and error histograms.