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Model of a nonlinear reaction system with autocatalysis and autoinhibition: Stability of dynamic states

Nelinearni reakcioni sistem sa autokatalizom i autoinhibicijom - stabilnost dinamičkih stanja

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2012
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Authors
Maćešić, Stevan
Čupić, Željko
Kolar-Anić, Ljiljana
Article (Published version)
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Abstract
Self-regulation, achieved through positive (autocatalytic) or negative (autoinhibitory) feedback is commonly encountered in natural, technological and economic systems. The dynamic behavior of such systems is often complex and cannot be easily predicted, necessitating mathematical modelling and theoretical analyses. The aim of this work is to analyze the dynamics of a minimal model system with autocatalytic and autoinhibitory steps coupled through the same species, in order to understand under which critical condition the system loses stability and passes through an Andronov-Hopf bifurcation. The analysis used was improved stoichiometric network analysis (SNA) in combination with bifurcation and sensitivity analysis.
Većina realnih sistema su nelinearni, zbog čega je ispitivanje nelinearnih sistema od velikog značaja za različite oblasti nauke. Među navedenim sistemima posebno su značajni nelinearni reakcioni sistemi sa povratnom spregom (autokataliza i autoinhibicija), za koje su karakteristične pojave kao što su oscilatorna evolucija ili haos, i koji se mogu sresti u prirodnim, tehnološkim i ekonomskim sistemima. Kako se autokataliza i autoinhibicija često istovremeno mogu naći u realnim sistemima, mi smo analizirali stabilnost jednog reakcionog modela u kome su ova dva procesa spregnuta i pokazali kako stabilnost ovog sistema zavisi od konstanti brzina i koncentracija hemijskih vrsta koje su uključene u model. Nelinearni procesi sa povratnom spregom i odgovarajući modeli uglavnom imaju veliki broj promenljivih, zbog čega analiza stabilnosti zahteva upotrebu posebnih matematičkih alata. Za izvođenje analize stabilnosti ispitivanog modela, koristili smo unapređeni metod stehiometrijske mrežne anal...ize (SNA) u kombinaciji sa bifurkacionom analizom i analizom osetljivosti. Koristeći navedene metode analize, uspeli smo da izdvojimo reakcije koje predstavljaju jezgro nestabilnosti i koje su odgovorne za periodičnu evoluciju sistema, na osnovu čega smo uspeli da odredimo uslov koji je neophodan za postojanje Andronov-Hopf bifurkacije.

Keywords:
nonlinear dynamics / stoichiometric network analysis / autocatalysis / HPA system / Andronov-Hopf bifurcation / nelinearna dinamika / stehiometrijska mrežna analiza / autokataliza / HPA sistem / bifurkacija Andronov-Hopf
Source:
Hemijska industrija, 2012, 66, 5, 637-646
Publisher:
  • Association of Chemical Engineers of Serbia
Projects:
  • Dynamics of nonlinear physicochemical and biochemical systems with modeling and predicting of their behavior under nonequilibrium conditions (RS-172015)
  • Nanostructured Functional and Composite Materials in Catalytic and Sorption Processes (RS-45001)

DOI: 10.2298/HEMIND120210034M

ISSN: 0367-598X

WoS: 000314735800002

Scopus: 2-s2.0-84869442639
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URI
http://cer.ihtm.bg.ac.rs/handle/123456789/1079
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