000108672 001__ 108672 000108672 005__ 20211216104751.0 000108672 037__ $$aTAZ-TFM-2021-457 000108672 041__ $$aeng 000108672 1001_ $$aMayora Cebollero, Ana 000108672 24200 $$aCoupling and Chaos: a Mathematical Analysis of the Two-Coupled Brusselators Model 000108672 24500 $$aAcoplamiento y Caos: un Análisis Matemático del Modelo de Dos Brusselators Acoplados 000108672 260__ $$aZaragoza$$bUniversidad de Zaragoza$$c2021 000108672 506__ $$aby-nc-sa$$bCreative Commons$$c3.0$$uhttp://creativecommons.org/licenses/by-nc-sa/3.0/ 000108672 520__ $$aThe Brusselator is a theoretical model that represents a type of autocatalytic chemical reaction with oscillations. The interaction between two Brusselators (coupled by diffusion) is described by the two-coupled Brusselators model. This model has at least one equilibrium point (in some regions of the parametric space there are up to four more equilibrium points) and undergoes a pitchfork and two saddle-node bifurcations under certain conditions.<br />There are 4-dimensional nilpotent singularities of codimension 4 that are unfolded by the system of the two-coupled Brusselators. In any generic unfolding of such singularities there exist 3-dimensional nilpotent singularities of codimension 3 which are generically unfolded by the same family. <br />As Shil'nikov homoclinic orbits exist in any unfolding of a 3-dimensional nilpotent singularity of codimension 3, these homoclinic orbits are present in the two-coupled Brusselators model. The existence of this type of homoclinic orbits implies the presence of strange attractors in a model. Therefore, the two-coupled Brusselators model contains strange attractors. <br />The two-coupled Brusselators model is chaotic in some regions of the parametric space.<br /><br /> 000108672 521__ $$aMáster Universitario en Modelización e Investigación Matemática, Estadística y Computación 000108672 540__ $$aDerechos regulados por licencia Creative Commons 000108672 700__ $$aSerrano Pastor, Sergio$$edir. 000108672 700__ $$aLozano Rojo, Álvaro$$edir. 000108672 7102_ $$aUniversidad de Zaragoza$$b $$c 000108672 8560_ $$f735935@unizar.es 000108672 8564_ $$s8621422$$uhttps://zaguan.unizar.es/record/108672/files/TAZ-TFM-2021-457.pdf$$yMemoria (eng) 000108672 909CO $$ooai:zaguan.unizar.es:108672$$pdriver$$ptrabajos-fin-master 000108672 950__ $$a 000108672 951__ $$adeposita:2021-12-16 000108672 980__ $$aTAZ$$bTFM$$cCIEN 000108672 999__ $$a20210627194415.CREATION_DATE