Weakly reversible mass-action systems with infinitely many positive steady states

We show that weakly reversible mass-action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible and has a single connected component. In our construction, we relate operations on the reaction network to the multivariate polynomial occurring as a common factor in the system of differential equations

Permanence of Weakly Reversible Mass-Action Systems with a Single Linkage Class

We give a new proof of the fact that each weakly reversible mass-action system with a single linkage class is permanent

Reaction Networks and Population Dynamics

Reaction systems and population dynamics constitute two highly developed areas of research that build on well-defined model classes, both in terms of dynamical systems and stochastic processes. Despite a significant core of common structures, the two fields have largely led separate lives. The workshop brought the communities together and emphasised concepts, methods and results that have, so far, appeared in one area but are potentially useful in the other as well

Dynamical Systems; Proceedings of an IIASA Workshop, Sopron, Hungary, September 9-13, 1985

The investigation of special topics in systems dynamics -- uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory -- has become a major issue at the System and Decision Sciences Research Program of IIASA. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under variations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of nonlinear dynamic systems theory to biomathematics and ecology. The proceedings of a workshop on the "Mathematics of Dynamic Processes", dealing with these topics is presented in this volume