Mathematics

Interactional Analysis of a Regional Based Multiple Organic Farming System on an Activity Induced Fertility Varying Soil Resource

Abstract

This study presents a system of deterministic mathematical models that describes regional agronomy and the conservational dynamics of organic farming on activity-induced-timevarying soil resource. Major incorporates include advocacy and environmental enlightenment, challenged-based conservational strategies, crop/livestock densities and their ensuing interactions with the various soil conditions, crop/livestock removals, manure generation, decomposition and absorption, non-agricultural land utilisation and the various requisite stabilisation dynamics for each soil condition. We performed both the interactional and stability analyses with a view to assessing the individual contributory-potentials of the components of an organic farming process. We obtained the basic degradation ratio for each soil condition and the various conditions for both local and global stabilities of the various challenged – free equilibria aptly established. Using the centre manifold theory, bifurcation analyses across the models revealed the forward type. Further, sensitivity analyses, buttressed by numerical simulations, distinguished the sensitive relevance of parameters. Manure utilisation impact on conservation indicated an optimality that is sensitive enough for an emphatic contemplation on a wide scale adoption. Conversion of formerly agricultural lands to non-agricultural purposes indicated a substantial positive impact on reclamation. Excessively deploying efforts on the soil beyond the allowable threshold depletes soil fertility and that a well-informed combination of conservation strategies has the enormous potential to improve the chances of increasing productivity. Sensitively analysing the baseline parameters using the normalised forward sensitivity index, further plausibly suggested the impracticability of the entire land mass of the study area to erode, the comparability of correcting infertility than erosion and further emphasised the inherent potentials of NALU to soil conservation and reclamation. The unrestrictive nature of the models has inherently extended their applicability to investigate external farm input, especially those with depletive chemical configuration.