THE PREICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS INTROUCTION The wo dmensonal paral dfferenal equaons of second order can be used for he smulaon of compeve envronmen n busness The arcle presens he deducon of equaon necessar for calculaon eplans he used varables and her nerpreaon n he compeve envronmen The frs es case eplans he wa of he use and calculaon and he second case presens he applcaon n pracce The mehod can be used for he buld up of a model of compeve envronmen n he feld of markes banks frms suppler-cusomer relaons ec THEORY Two dmensonal paral dfferenal equaons of second order wll be used for smulaon of compeve envronmen n he form ) I s necessar o ransform he equaon o a suable form for numercal compuaon The equaon of he dervaon of he frs order has he form ) The equaon of he dervaon of he second order has he form ) 3) The equaon of he frs order for dervaon of me can be wren n he form 4) The paral dervaon equaon of he frs order of varable can be wren n he form 5) and for varable 6) The equaon of he paral dervaon of he second order for varable has he form ) 7) and for varable
) 8) We can wre he equaon n he followng form when we use he prevous equaons 4) 7) 8) ) ) 9) When we se up he condon we can rewre he equaon 9) n he followng form ) ) [ ] ) 0) If we subsue ) ) we can wre he fnal equaon n he form ) ) [ ] ) Ths equaon can be used for he buld up of compeve envronmen model 3 BUIL OF THE MOEL The meanng of used varables n he problems of buld up of a model of compeve envronmen s as follows: The values of cells of compeve envronmen wh nde of me and ssem of coordnaes are presened b he range from 00% o -00% where 00% means mamum negave compeve envronmen and -00% means mamum posve compeve envronmens The value 0% means neural compeve envronmen The defnon of varable of compeve envronmen depends on a concree applcaon I can be defned for eample b he coun of clens of banks frms companes and he coun of nhabans n owns vllages ec The varous couns and her changes creae he compeve envronmen The varable for compeve envronmen has he frs dervave of compeve envronmen ha presens he flow of he compeve envronmen and he second dervave presens he acceleraon of compeve envronmen The value s a smulaon consan The consans and presen he rae of spread of compeon envronmen n drecon of and Each cell O s coded n he followng manner: a) an nfluence on compeve envronmen ecep nal condon) b) sold obsacle an nfluence on compeve envronmen) c) posve and consan nfluence on compeve envronmen d) posve and varable nfluence on compeve envronmen e) negave and consan nfluence on compeve envronmen f) negave and varable nfluence on compeve envronmen The program was desgned for he smulaon of he compeve envronmen The npu values are consans mar 0 n m) nal condons of compeve envronmen of each cell n me T 0 0) mar On m) code of each cell) The las em s he me T end he end me of calculaon of compeve envronmen 4 TEST CASE
The process of se up of npus and presenaon of resuls of calculaon of he desgned program s done va dspla The descrpon of he screen of a program wh es daa s presened n fg The rgh sde of he screen enables o se up he me T end [Tme] he end me of calculaon of compeve envronmen) he dela [ela] beween seps of calculaon for dsplang when he seppng s allowed The check bo [Graph] deermnes wheher he daa are dsplaed n he form of fgures s enabled onl for he mar up o dmenson 00 here are dsplaed he codes of cells her nal and fnal values of compeve envronmen ) or b colours onl he mar of envronmen compeon s dsplaed n colours) The check bo [Sep] deermnes wheher he resuls of he sngle sep of calculaon are dsplaed wh he se up dela [ela] or onl he end sae The course of value of compeve envronmen of concree cell n me can be recorded no he fle b seng s coordnaes and [Hsor record X-as Y-as] The dsplaed value [Sep No] nforms abou he process of calculaon whch sep s done The choce of se of daa can be made n fle bo The sar of calculaon s done b buon Sar The sop of calculaon s done b buon End Fg The screen of a program wh he use of fgures The es case s presened b he mar of 00 dmensons The lef upper sde of he screen shows he mar O00) of codes of cells he lef mddle sde shows he mar 0 0 0) of nal values of compeve envronmen n me T 0 0 and he lef lower sde shows he mar of resuls of end values of compeve envronmen end 0 0) 80 n me T 80 80 Fg presens he es case where he values of he compeve envronmen are n colours on he lef sde of he screen The specrum of colours s used from red 00%) hrough ellow 0%) o green -00%) The scale of colours presenng he value of compeve envronmen s dsplaed on he rgh par of he screen The cells wh non zero nal condon of compeve envronmen are marked b leer a and he were se o mamum negave compeve envronmen 00) he sold obsacle s marked b he cell of posve and consan nfluence on compeve envronmen s marked c he cell of posve and varable nfluence on compeve envronmen s marked d he cell of negave and consan nfluence on compeve envronmen s marked e and he cell of negave and varable nfluence on compeve envronmen s marked f Ths es case presens all possble suaons 3
e a d c f b a e Fg The screen of es case of compeve envronmen Each cell has a colour s value corresponds wh he value of he compeve envronmen afer calculaon T 80 80) from green va ellow o red The suaon n end me T 80 80) s as follows Some cells have negave some posve and some neural nfluences on he compeve envronmen Fg3 presens he course of value of he compeve envronmen of he cell wh coordnaes 9 and 5 n me marked as cell f and place Brno I s suable o evaluae he frs dervave of compeve envronmen ha presens he speed of change of value of compeve envronmen and he second dervave ha presens he acceleraon of change of value of compeve envronmen I enables o make an evaluaon n a greaer deal Compeeve Envronmen 60 Compeeve envronmen ' '' [dos dos/s dos/s-] 40 0 0-0 -40 6 5 76 0 6 5 76 0 6 5 76 ' '' -60 as [-] Fg3 The behavour of compeve envronmen n me 4
The graph presens he fac ha he hgh negave value of he compeve envronmen s decreasng n me and connues o be neural furher connues o be posve and ends nearl neural The course of value of he compeve envronmen s no smooh here are some seps) because of buld up model wh chaoc and random behavour ecep deermnsc 5 REAL CASE The real case presens he suaon of compeve envronmen presened among EU naons represened b capal ces such as Amserdam Berln Bern Braslava Brussels Budapes London Lublana Luemburg Pars Prague Vaduz Warszawa Venna and Zagreb Some ces have posve nfluences such as owns of new EU saes Some ces have negave nfluences of compeve envronmen such as old EU saes The suaon presens he sruggle for new errores n busness Fg4 presens such suaon b means of colours afer 00 das Prague Fg4 The screen of program wh he use of colours Conmpeeve envronmen [dos] 30 0-0 -30-50 Compeeve Envronmen 4 6 8 as [-] Fg5 The behavour of compeve envronmen n me 5
The process of calculaon of he compeve envronmen s a dnamc process where he me plas an mporan role Therefore s suable o search for he behavour of cells from he pon of values of compeve envronmen n me The course of value of compeve envronmen of he cell wh coordnaes 8 and 5 n me s presened n fg5 and s marked as a cell of Prague n Czech Republc The graph presens he fac ha he hgh posve value of he compeve envronmen s decreasng n me and ends o be slghl negave compeve envronmen Some cells can have consan behavour ohers have behavour ha s dependen on me Ths dependence can be generaed b an funcon Oher dependence can be creaed b chaoc or pseudorandom generaor The cells nfluence each oher Ther muual nfluence s descrbed b paral dfferenal equaon of he second order ha was menoned n he chaper dealng wh heor 6 CONCLUSION The menoned newl desgned mehod n he arcle s focused on he feld of busness and econom where he compeon envronmen plas a ver mporan role Ths mehod of he buld up of a model and s realzaon b suggesed program enables he search for compeve envronmen ha could be ver mporan and s resuls can be used for decson makng processes The calculaon can preven grea losses Ths nal research wll be furher developed dealed and esed The desgned mehod can be used n he feld of markes banks frms suppler-cusomer relaons ec 6