IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728,p-ISSN: 2319-765X, Volume 7, Issue 6 (Sep. - Oct. 2013), PP 100-105 www.iosrjournals.org www.iosrjournals.org 100 | Page Penalty Function Selection Method Of Best-Fit Model Parameters Of Interacting Agricultural Crops In Oil Uncontaminated Utisol:Part 1 E.N. Ekaka-A, C.C. Wokocha, N.M. Nafo, E.H. Amadi, E.C. Nwachukwu, A. Musa, I.A. Agwu, Department Of Mathematics And Computer Science, Rivers State University Of Science And Technology, Port Harcour t, Department Of Crop And Soil Science, Faculty Of Agriculture, University Of Port Harcourt, Nigeria, Department Of Mathematics And Computer Science, Rivers State University Of Science And Technology, Port Harcour t, Department Of Mathematics And Computer Science, Rivers State University Of Science And Technology, Port Harcour t, Department Of Mathematics And St a tistics, University Of Port Harcourt, Port Harcourt, Nigeria, Department Of Mathematics And Statistics, University Of Port Harcourt, Port Harcourt, Nigeria, And Dep ar tment Of Mathematics, Abia State Polytechnic, Aba, Nigeria Abstract: The time series data of interacting legumes grown in oil uncontam- inated utisol have been collected. However, the dynamics of a best-fit math- ematical model that can be used to describe the interact ion between cowpea and groundnut poses a challenging interdisciplinary approach. We propose to use the 1-norm penalt y function method to select the best-fit model parame- ters from a list of other candidate logistic models. A mathematical analysis of this best-fit interspecific interaction model will be conducted. The novel results which we have achieved in this study will be presented and discussed. Key words: and phrases. Best-fit parameters, agricultural data, 1-norm. I. Introduction This simulation st udy is based on the current data which was collected by two experts in microbiology who are working in the Niger Delta Region of Nigeria ([1]). In their research report, the growt h data of cowpea and groundnut over a growing season in weeks were provided in an uncontaminated utisol were obtained. However, their focus of research was not on numerical simulation analysis which uses the not ion of the three popular mathematical norms to select the best-fit model parameters which characterize the interact ion dynamics between cowpea and groundnut. There is an extensive collect ion of literat ures on themes which relate to plant - plant int eractions, modelling biological interact ing populat ions, equations of det er- minate growt h and plant growt h analysis to mention a few ([3]; [4]; [5]; [6]; [7]; [8]; [9]; [10]; [11]; [12]). All these useful citations deal more wit h clearly defined model formulations which indicate sufficient ecological insights. However, the application of which selection met ho d is used to select the best -fit model parameters is rarely a computational approach. Because of the sophistication of measuring the agreement between provided data and simulated data over a time int erv al which is usuall y taken for grant ed in most parameter estimation analysis of biological interact ion data, we will attempt to define the metho d of penalt y function select ion met ho d ot her wise called the cost function select ion met ho d in this paper. We would think that t here may be some environmental pert urbations and other features of the eco- logical instabilit y which might change the best -fit behaviour between the given data and simulated data which we do not propose to model in this present simulation study . Given these data on the growt h of legumes ([1]), it is a challenging scientific prob- lem to construct a mathematical model which describes the dynamics of any two interacting legumes wit hin an uncontaminat ed environmental sett ing. Attempting to develop t hese distinct nonlinear model equations will provide crop scient ists wit h useful information such as the growt h rates for two types of legumes, the intraspe- cific coefficients of legumes and their mass law action or interspecific coefficients as is popularly known in mathematical biology and molecular physics. The informa- tion about the doubling times of the two interacting legumes is an important insight which will assist further research in