Competition between Robust and Nonrobust Autocatalytic Replicators

Abstract

The competition of two species for a common resource is illustrated using the paradigm of autocatalytic replicators inhabiting a continuous stirred tank reactor (CSTR) environment that is continuously fed with the resource. In most cases presented, one species is robust (appears in reactor feed) while the other is not. The introduction of the second (invading) species into the CSTR via an unsustained disturbance has a strong effect on the steady-state and dynamic behavior of the first (host) species. New steady states are added to the bifurcation diagram that show that the invading species can coexist in the system with the host species when its growth and death characteristics are similar to those of the latter. The population levels of the host species are greatly reduced in these cases as a result of the considerable decrease in resource concentration at steady state. Open-loop strategies for the elimination of the invading species are developed and discussed. These strategies involve the manipulation of the reactor residence time to destabilize the states of coexistence.

Autocatalytic reaction on low-dimensional substrates

“…the reaction is strictly local and deterministic. Autocatalytic reactions have been extensively analyzed on Euclidean structures, both analytically and numerically [10,11,12,13,14,15]. A continuous picture of this system can be attained by the Fisher equation [16,17] which describes the system in terms of front propagation; however, this picture will not intervene in our calculations, that will mostly concern the low-density regime, where a front propagation cannot be defined.…”

Reconfiguration of chemical reactor networks using a hierarchical agent-based system

“…Consequently, if the control objective calls for one species to be replaced with another, a nonlinear control scheme must be used. For a single CSTR with competing autocatalytic species, one strategy may be to modify the reactor residence such that the undesirable species is washed out of the system, and then set to an appropriate value that is favorable to the existence of the desired species [5], [6]. Obviously, there is usually more than one strategy to achieve such control objectives.…”

Agent-based system for reconfiguration of distributed chemical reactor network operation

“…For a single CSTR with competing autocatalytic species, the reactor residence time must first be modified such that the undesirable species is washed out of the system, and then set to an appropriate value that is favorable to the existence of the desired species [10], [11]. This concept can be extended to systems with many reactors to effectively control the spatial distribution of autocatalytic species in the network.…”