Gabaliem lineāru diferenču vienādojumu sistēmu uzvedība
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Latvijas Universitāte
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lav
Abstract
Bakalaura darbā tiek apskatı̄ta noteikta veida gabaliem lineāru divu diferenču vienādojumu sistēmu uzvedı̄ba. Tiek pierādı̄ts, ka visi sistēmas atrisinājumi ir eventuāli lı̄dzsvara punktam. Darbā ir atreferēti raksta [5] rezultāti, kas papildināti ar izvedumiem, ilustrācijām un piemēriem. Saistı̄bā ar šo rakstu tiek analizēti citi iespējamie apskatı̄tās sistēmas gadı̄jumi atkarı̄bā no parametriem b un d. Tiek atrasti lı̄dzsvara punkti un izvirzı̄tas hipotēzes par sistēmas atrisinājumu izsturēšanos atkarı̄bā no parametriem. Vienā no gadı̄jumiem ir izdevies pierādı̄t atrisinājuma ar periodu 7 eksistenci.
In this paper a certain type of system of two difference equations is examined. It is shown that all solutions of the system are eventual to the equilibrium point. The results of the paper are reincounted and supplemented with expansions, illustrations, and examples. In relation to [5] other possible systems were examined depending on the parameters b and d. The equilibrium points were found and hypothesis about the behaviour of the system depending on the parameters were made. In one of the cases it was possible to prove the existence of a solution with period 7.
In this paper a certain type of system of two difference equations is examined. It is shown that all solutions of the system are eventual to the equilibrium point. The results of the paper are reincounted and supplemented with expansions, illustrations, and examples. In relation to [5] other possible systems were examined depending on the parameters b and d. The equilibrium points were found and hypothesis about the behaviour of the system depending on the parameters were made. In one of the cases it was possible to prove the existence of a solution with period 7.