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Modeluvannya ekonomiki - Vіtlіnskiy V.V.

2.1.2. Specifics, the principle of mathematical modeling

Modelyuvannya є process of incentives, vivchennia that zastosuvannya models. Vano podegnane with such categories, as abstraction, analogy, hypothesis tochno. Process modulyuvannya obovzyazkovo include konstruyuvannya naukovyh gipotoz.

The main peculiarity of modeling is the fact that one has the method of indirectly recognizing for oboektomu ob'ektiv-zamishchuvachiv. The model is post-yak sovietnyj інструмент пізнання, що його дослідник (системний аналітик) put між сооєю that об'єктом і for допомогою якого вивчає об'єкт, який його цікавить. Same tsya soblivіst modelyuvannya viznachaє tekhnicheski form vikoristannaya abstracts, analogy, gipotoz, інших категорій і методиів пізнання.

Necessity of vichorennya modulyuvannya viznachaetsya tim, scho bagato ob'ektiv (chi aspectiv, yakі stosuyutsya tsikh ob'ektiv) without any meddling, chi vzagali nelmozhlivo, chie vimagaje bahato chasu i koshtiv.

Nehai є chi nehhіdno make a very active obekt A. Mi konstruyuemo (materially chi in uyavi) abo is known in the real world of the present B -model of object A. Можна виокремити такі чотири основні етапи побудови models.

The first stage of perebacha nayavnіst active people know about ob'ekt-original. Пізнавальні можвності моделі змовлюються тим, що model відображає, з погляду системного аналітика, суттєві риси об'єкта-оригіналу. Feeding about neobhіdnіst і richestvnost podіbnotі origіnіnalu і modelі need analizu. Obviously, the model vtrachaye sen syak y vipadku totozhnostі z originalalom (TODI vona do not cease to be original), so in different nadmirnyi in usіh suttievi vidnoshennykh proskischenya. Вивчення certain authorities of the model of the subject matter відбувається за рахунок відмови від відображення інших сторін. Through tse be-yaka model zamishchuyu origignal tilki in strictly obmezhenomu sensei. Із цього випливає, що for one ob'ekta mozhe bouti the decil "specialization" of models is stimulated, yakі to concentrate respect on the singing sides of the prejudiced object of the chi characterize the subject of the rіznim рівнем Detailізції.

On another model, the post-yak is the self-contained objec- tive. One of the forms of such a dosage is the conduct of "model" experiments, for which it is possible to change the function of the model and systematize the information about the "behavior". Residual result of this stage is the factor know about the model B.

On the third stage, you can transfer the transferred one from the model to the origi- nal - the form of the multiply know S about the object. Tsey the process of transferring know to be held behind the singing rules. Knowing about the model makut bouti skorigovaniem z urahuuvannya mikh vlastovosti ob'ekta-originalu, kotry not znaydli vidobrazhennya chi buli deformovaniemi pid hour of the model. Mi mozhemo z dostatnoyu pіststavoyu pokasiti yakiy-nebud result from the model on the original, yakshchoy zey result obovvjazko kovyazyaniy z znakami podobnoti originialu th model. Yakshozh the first result of the model report on the situation in the model of the original, then yogo carry unjustly.

The fourth stage is a practical change in the models for knowledge of models of knowledge for the sake of morality, for the motives of the legal and economic theory of control.

For rozumnіnya sutnostі modulyuvannya importantly mother on uvazi, sho modelyuvannya - not єdine dzherelo otrimannya novi know about ob'ekt. Process modulyuvannya "zanureny" in bilsh zagalnyh process piznannya. Tse vrahovuyutsya is not deprived at the stage of the model's motivations, but on the final stages, if the admission is made, and the results of the work are fulfilled, you must adhere to the piсnomіnі of різноманітних засобів пізнання.

Modelyuvannya - cyclical process : for the first chotiriohetapnim cycle mozhe by the way, another, tretiy tescho. With the knowledge of the information about the contents of the site, it can be specified, but the vihid model is post-paid. Недоліки, які виявляються після першого цилу моделювання, що змовлені, наприклад, недостатнім вивченням об'єкта и помилками в побудові model, you can turn in the oncoming cycles. Methodology modulyuvannya, such a rank, zakladeni mozhnolisti samorozvku.

Signifi- cantly, three times ignorant are three steps to the motivations of mathematical models. Methodically, the pi-ad is written that skerovot on the transition from simple to collapsible.

The first is the actual situation. Suttveve prodyschenya reach todi, if you are power-hungry, you will not get into the trouble of getting tired of doing so. Otzhe, folded for its nature, practical situation is to be looked at before the analogical analogue, a kind of mathematical description.

The other is motivated simply by the models on the pidstavi of the singers, nicharakterninnihspecialities of real situations, with the approaching poslidninnam takoї model haylennya інших чинників right up to отримання "прийнятного" варіанта моделі.

Тretій - entered in the well-known кількості чінників у їхніх взаємозв'язках 'and і пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ In the skin vipadku model "rozvivaetsya" ta clarify at the world dosyagnennya glibshego rozumninya system analitikom sutnosti posavlenoї problemy ta ob'ekta doslenia.

Systematic analitiki zobov'yazi keruvatisya takozh principles shodo kontseotsії "mathematical model" of the active obekta.

Principle 1. The dialectic couple model-ob'ekt zavzhdi polar, moe two poles - "model" and "ob'ekt."

Principle 2 . Z dvuh vzajmopov'yanyh polysіv dialektichnoy betting model-ob'ekt one є prinimnym, іnshy - pohіdniy vіd nyogo.

Principle 3. The presence of the pole "ob'ekt" is not sufficient for the presence of the pole "model", the presence of the pole "model" zoumovlyu neobhindnost nayavnosti pole "ob'ekt."

Principle 4. Yak "model" for this "ob'ekt", so "ob'ekt" for the given "model" is semantic and intrapreciative: "model" vidzzerkalyuet vlastotvosti not one, but bugatokh "ob'ektiv", "about "Єкт" is described not as one, but as "models".

Principle 5. The "model" is guilty of an adequate "objektov" vidobrazhati z pevnoyu podnnistyu ynogo yogo risi ta vlastovost v zdalo vіd tsіley doslіdzhennya, nayavnії іnformatsії priinyatnoyї sistemi gipotoz.

Warto zaznachiti, scho on praktitsi realizuyut three basic steps of formalizatsii (formovannya mathematicheskogo model): zmistovnyh opis; Formalized scheme; Mathematical model.

I will look at the results of the dosage, the meta-model of the models of the model of the empirical situation, the "task" (dosleness), the shifting of the elliptic analisation, the obtuse point of the iko zmistovnyi description of the obviect (apparition, process). On the verbal rivnі (movable zasolami) vіdtoryuyutsya dany about the nature (сутність) об'єкта, кількісні characteristics явищ (progressів), які спостігаються, nature взаємодії між warehouses елементами, місце та важіість skinny явища in the fatal process of the function of the ob'ekt dostlenia. On the basis of the zymistovogo description, the formalization is to be carried out before the vio-cremation of the many suttiviks (keyoviks), which characterizes the subject (y zidіdno in the method of the doslenie and impulses of the model), the yogo structure, the authorities, the spivvodnoshennya mizh warehouse members. Кожен з виокремлених чинників is guilty of buti descriptions on the yakіsnomu ta kіlkіsnomu рівнях (the interval mozhlivih znachen, scale vimiryuvannya tochno). Formo zmistovogo opizu mozhe bouti terminologicheskii vysliv, text, sukumnnist number of values ​​with a commentary.

Parallel Zi zmіstovnim inventory (chi descho pіznіshe) Mauger formuvatisya scheme, yak at viglyadі simvolіv, grafіkіv, grafіv, Table zobrazhuє perelіk that vzaєmozv'yazki schodo viyavlennya suttєvih chinnikіv so dwellers Nadachi їm tsіlіsnіst, KOTRA used in zagalnih risah vіdtvoryuvala (adequately) vlastivostі Ob'ekta doslenie. The laws of this law can be made with opisovymi virazy, nazvi - mathematic symbols, vidnoshennya - mathematical dia (operators).

A long way to re-authorize the written description of the formalized schema in the group of mathematic symbols and to complete the motivation of the mathematical model. Exposure The zakonіv i zakonomіrnostey "materіalіzuєtsya" through rules that formalnoї logіki logіchnogo vivedennya in formі rіvnyan, nerіvnostey, spіvvіdnoshen mіzh ically mathematical symbols s tochnіstyu to іstinnostі ically mathematical peretvoren that vіdpovіdnostі schodo sformulovanih gіpotez real laws. Such a model is the mathematical model of the pre-linguistic objekt of subordinates up to one's ob'ektiv-analogues.

Існують різні форма зобрабраня математичної моделі. Різновид їх to intervene chotirma to findpopy groups - innovative, algorithmic, analitic, schematic.

Інваіантна form - the image of the mathematical model without a priori to the methods, for the sake of what can be rozv'zavatis the task of modeling is set.

Applied Inventory Form:

De a , b , c - the characteristics of the object; F ( Z , p ) is a function of the function; Y ( Z , p ) is an unknown function.

Algorithmic form - the image of the mathematical model in the vihliadі poslіdovnostі dіy, yakі neobhіdno vikonati, shcheb at rozv'yazannі posavlenyya problemyi modelyuvannya pass to the attention of the tribute to the joke result.

Application of algorithmic form:

• The values ​​of a , b , c are significant.
• Calculate d :

• Do you think d ? 0, then the calculation of the value of the result ( x , y ):

.

Analytic form - the image of the mathematical model in the formulations of the mathematics and mathematics, for the sake of some shukan in the tasks and modeling of the result, is viznachayatsya through vidomi dani.

Applied Analitic Form:

De a , b - відомі characteristics of the object, х - змінна, у - result.

The schema form is the image of the mathematical model in the tables of figures, diagrams, charts, graphs, graphs.

Application of the schematic form:

Here F 1, F 2 - transfer functions of the object.

Використання аналогів у побудові модели . Analogs in pobudovі models vikoristovuyutsya in velicheznіy kіlkostі vipadkіv: abo for sprobi pobuduvati model deyakogo ob'єkta, abo if nemozhlivo directly vkazati fundamentalnі Zakoni chi varіatsіynі principles Cauterets vіn pіdporyadkovuєtsya, abo if s Look sogodennih our knowledge vzagalі Absent vpevnenostі in іsnuvannі podіbnih zakonіv, To admit a mathematical formalization. One of the plural entries to this kind of ob'ektiv is the vicarities of analogies already with visions.

Zdalosya b, scho є spilnogo mizh radіoaktivnym rozpadom і dinamikoyu populyatsіy, zokrema, zmіnoju chiselnost 'populated area of ​​our planet? But on a simple rіvnі дослідження such an analogy to look through, about shcho svidchit one z nayprostіshih models populyatsіy - the model of Malthus. In pіdґruntі modelі Malthus - just tverdzhennya: shvidkіst zmіni chiselnostі population in t h hour proportsіyna yogo potochnіy chiselnostі N (t), on pomnozhenіy algebraїchnu scrip koefіtsієntіv narodzhuvanostі That death .

У результаті маємо рівняння

(2.1)

Yak is more like a peacock of a radiodiastic rospade and zbigajatsya him for the sake of a <b (yakshcho a i Postin). Tse not marvelously, for Vivodennya їh vikoristovuvalis odkoviv mirkuvannya. Інтегрування рівняння (2.1) since:

De N (0) = N ( t = t 0) is a small number of numbers.

Yakshto a = b, then the number of hours to fill up with a post, that in the form of vipadk rozvozyakom is the value of N ( t ) = N (0). Rіvnovaga mіzh narodzhuvanіstyu th smertnіstyu nestіyka rozumіnnі in fact, scho navіt are small torn down rіvnostі a = b s lead Pliny hour until all bіlshogo vіdhilennya funktsії N (t) od rіvnovazhnogo values N (0). For the reason a <b the population density of the population is reduced to zero, if t ® ?, and for a> b - the population is in the previous exponential law before nezinchennosti, yakshcho t ® ?. Ostanya obtanovana and servant pidstavoyu for obloyavan Malthus shodo majbutnyogo, pozvjazanyh zapraselennjam zemlі z sіima vyplivayuchimi zvіdsy naslіdkami. Yak at danomu application, so і in the lowest vypadkіv mozhna pokazati na chimal osmennyh obmezhen shchodo zastosuvannya pobudovanoї model. Zvichayno Well, the arc of the folding process of the Chisel of the Population, but to lie before that vvidomogo vtrychanya people themselves, can not describe yakimis forgive legitsirnostyami. Navіt in іdealnomu vipadku іzolovanoї bіologіchnoї populyatsії zaproponovana model is not vіdpovіdaє realіyam Povny mіroyu, Hoca used to zvazhayuchi obmezhenі resources neobhіdnі for її іsnuvannya. Zroblene zauvazhennya already nyak not use the role of analogy in the impulse of mathematical models of the arc of folding crannies.

It is nogolosimo, scho vikoristannaya analogy ґruntuyetsya on odnі z dozhe vzaimlivihh vlastostivosti models - їхній універсальності, тобто використанні їх schodo об'єктів principally різної nature. So, pripuschennia (heypothesis) type "shvidkist zmіni magnitudes proportional to the value of the self (for the deed of function)" is widely visored in economics.

Ієрархічний підхід to form models . Lisha in negagayoh vipadkah buvae zruchnuyu і vipravdanoyu podudova matematicheskih models navіt schodo pokhodih ob'ektiv vidrazu v usіy povnoti, z urahuvannyam usіh suttievih chinnikiv. This natural і підхід, шо realizes the principle "from simple - to folding", if the oncoming krok robitsya після досить detailed вивчення не дуже складної моделі. Otzhe, vinikaє lancyuzhok (ієрархія) усе більш детальлізованих models, кожна з яких узагальнює попередні, including yїk yak private vipadok.

Significantly, it is practical to practice the bank of models і здійснють adaption of the Відомої model.