Feasible Equilibrium in Kinetic Systems**This work received partial financial support through grants PIE201230E042 and Salvador de Madariaga (PR2011-0363) and PIE 201230E042

Antonio A. Alonso, Irene Otero-Muras
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4oklsgzkjvbihhegxblzc6b7re" style="color: black;">IFAC-PapersOnLine</a> </i> &nbsp;
In bridging theory and potential applications of chemical reaction networks, we adopt a geometric perspective to explore equilibrium in mass action law kinetic systems. Such systems are typically employed to model nonlinear dynamics in open and closed chemical reaction networks. As a class nonnegative systems, the range of potential applications extends far beyond chemistry to reach many processes and networks in natural and artificial systems. In this note we link network deficiency with
more &raquo; ... ation theory. In fact we find out that network deficiency determines the class of equilibrium multiplicity. For deficiency one networks a saddlenode bifurcation with respect to mass inventory is the only route to multiplicity whereas for higher deficiencies alternative routes exist which may include pitchfork bifurcation. Interestingly, some kinetic networks within this class are capable of multiple equilibrium for any reaction simplex. Abstract: In bridging theory and potential applications of chemical reaction networks, we adopt a geometric perspective to explore equilibrium in mass action law kinetic systems. Such systems are typically employed to model nonlinear dynamics in open and closed chemical reaction networks. As a class nonnegative systems, the range of potential applications extends far beyond chemistry to reach many processes and networks in natural and artificial systems. In this note we link network deficiency with bifurcation theory. In fact we find out that network deficiency determines the class of equilibrium multiplicity. For deficiency one networks a saddlenode bifurcation with respect to mass inventory is the only route to multiplicity whereas for higher deficiencies alternative routes exist which may include pitchfork bifurcation. Interestingly, some kinetic networks within this class are capable of multiple equilibrium for any reaction simplex.
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