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Register a new userAnalysis of Mass-Action Systems by Split Network Translation
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Authors
Matthew D. Johnston
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We introduce the notion of corresponding a chemical reaction network to a split network translation, and use this novel process to extend the scope of existing network-based theory for characterizing the steady state set of mass-action systems. In the process of network splitting, the reactions of a network are divided into subnetworks, called slices, in such a way that, when summed across the slices, the stoichiometry of each reaction sums to that of the original network. This can produce a network with more desirable structural properties, such as weak reversibility and a lower deficiency, which can then be used to establish steady state properties of the original mass-action system such as multistationarity and absolute concentration robustness. We also present a computational implementation utilizing mixed-integer linear programming for determining whether a given chemical reaction network has a weakly reversible split network translation.
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This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of Chemical Reaction Network Theory, the Persistence Conjecture and the Global Attractor Conjecture. We study the persistence of a large class of networks called lower-endotactic and in particular, we show that in weakly reversible mass-action systems with two-dimensional stoichiometric subspace all bounded trajectories are persistent. Moreover, we use these ideas to show that the Global Attractor Conjecture is true for systems with three-dimensional stoichiometric subspace.
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This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global exponential stability are established for this class of systems under arbitrary switching which satisfies some assumptions on the average dwell time. The obtained criteria are shown to cover and improve many previously known results, including, in particular, sufficient conditions for absolute exponential stability of switched time-delay systems with sector nonlinearities. Some simple examples are given to illustrate the proposed method.
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