Optimal Use of Fertilizer to Overcome the Effects of Toxicity in Plants

Tapan Kumar Kar,Ashim Batabyal

doi:10.5539/jmr.v2n2p85

Abstract

In this paper we have considered a two species competitive system where one species produces a substance, which is toxicto the other. Various equilibrium points and their stability are discussed. Optimal policy of using fertilizer is determinedby means of control theory. Finally, some numerical simulations are given.

Highlights

Plant-plant chemical interference play an important role in nature
It is common experience that there are two types of such interference (i) direct plant - plant interference mediated by allelo chemicals, and (ii) the effect of secondary compounds released by plants on abiotic and biotic soil processes that effect other plants
The most important effects of compounds released into the soil environment by plants on other plants occur through indirect effects

Summary

Introduction

Plant-plant chemical interference play an important role in nature. It is common experience that there are two types of such interference (i) direct plant - plant interference mediated by allelo chemicals, and (ii) the effect of secondary compounds released by plants on abiotic and biotic soil processes that effect other plants. We know that if we try to grow tomatoes near black walnut (juglans nigra), we face the devastating effect the chemical juglone can have on certain plants. Both blackwalnut and butternut (J.cinerea) produce juglone in sufficient amount to cause wilting and yellowing of leaves, and sometimes the death of the entire plants. Sometimes due to shortage of land, it becomes necessary to grow different plants even if they do not maintain the normal distance between them In such case, the problem is to see whether proper dose of fertilizer could be ascertained which would ensure the optimal growth of the plants in the best possible way. Many studies have been developed to better understand the effect of toxicants on populations ( Barrett (1983), Hallam and Luna (1984), Luna and Hallam (1987), Bhattacharya (2004), Hallam et al (1983), Chatterjee (1996), Tillmann and John (2002), Das et al (2009), Sole et al (2005))

Mathematical Models

Bionomic Aspect of the Model